This question really isn't for me (I'm married), but on behalf of a single relative. How likely is it for a couple to achieve a good, peaceful marriage if they bring in children from previous relationships?
It depends on the couple and how they relate to each other with this dynamic. People like my father, who married my mother who had a child with another man before they met, jump into it swimmingly and have no problems on that front. Others, there are adjustments.
My brother is what I consider a strong Christian, and he is pursuing a biblical courtship with a Christian girl. They are both young (early twenties) and had rough pasts, but are committed to Christian lifestyles now. My brother has no children, but the girl has a two-year-old boy. She is the primary caretaker, though the father is involved too. He is remarried with other children already. My brother gets along fine with the little boy, though he has no major role in his life at this point. He's rather indifferent about children - treats them well, but doesn't particularly like or dislike them, and definitely has no experience with them.
The thing that sticks out to me here is indifference towards the child. When you date somebody with kids where you think there's a future, you can't really be indifferent towards them. You're entering into a relationship with them too, not just the parent. If you're not feeling any affection towards them, or something stronger than indifference, that's going to be a huge stumbling block or issue later.
Now maybe they're not at the point where a relationship with the child is really involved, or they haven't met yet, or maybe things need to get more serious... That I get. But at some point before they start talking commitment, you've got to get involved with the child, if anything so you can see how the dynamic of insta-parent works for you.
Do you think it would be difficult to start off a marriage with a two-year-old in the household?
Starting a marriage is difficult anyway. This can potentially make it moreso. That's why before one gets to a point where they're talking about marriage, you've got to be involved with the child.
Is it hard to parent or agree on parenting decisions when you're not the legal parent?
When you marry somebody with kids, you're not just marrying the parent, you're marrying the child too. To a degree, you're also marrying the ex. A lot of what you do will involve considering/working with the ex, and all of it will involve working with the child.
Is it hard to make parenting decisions when you're not the birth parent regarding your spouse's child? It's as hard as it would be with a child you share... For us, it's not really a big deal. If you have a healthy relationship with each other, then it's not a big deal at all.
Is it hard to make parenting decisions when you're not the birth parent regarding your spouse's child with the child's other parent? Potentially, yes, it's insanely difficult. It all depends on the type of person your spouse's ex is, how they view you, how you interact with them, how they interact with your spouse, how involved are they with the child, etc etc.
For example, my sister lived hundreds of miles from her Dad. He was not exactly passive, but not the most active father either. She'd visit once a year, no holidays, but could call him (and he'd call) whenever. The only conflict my father ever had with raising my sister was when her father would make arraignments to see her. Obviously, they'd see each other in the summer, when she didn't have school, but her Dad wanted her for a majority of the summer, whereas my Dad resented that he just waltzed in once a year, picked dates, and expected everybody to adhere to them, especially as those dates meant that she was gone for most of the summer. Since my Dad took vacations in the summer as well, it meant not seeing her at all during his vacations, during summer trips, etc. He felt since he didn't pay child support (and actually because he was broke, we paid for my sister to go and sent money for her care) and wasn't all that involved with her, that he couldn't make those demands. My mother was the great mediator and would inevitably talk her father down to a month with my sister, a month with us, and my father into understanding why the split time is so important. One conflict, that was it, per year. The only other conflict I remember was my Dad didn't want to co-walk my sister down the aisle. He never told her that, but it did really, really bother him as he did a majority of the raising of her. But other than that, my father accepted he was a father of hers as much as her biological Dad was, and her biological Dad accepted the same about my Dad. They were of equal authority.
Then there's my situation, where we share custody with the child's mother and we have to see her all the time. She even works with my husband. We see the kids 3-4 days a week and overnights, and they're very much a part of our household. She is a generally disagreeable person who likes to wrap up her wants with that of the kids and use them to try and guilt us into getting what she wants. For example, when it comes to setting the schedule of when they'll come over, she'll send a text that it'll be this date, time, this date, this time, and this date, this time. When we say that one of those dates don't work for us, immediately she'll say those are the only dates that work for her, nothing else will work, it has to be those dates and times. If we're firm again and say no, that won't work, then she'll accuse my husband of abandoning the kids, not treating them like a priority, being selfish, etc etc. When even that doesn't work (because inevitably the issue is she wants us to take them one day, we suggest another, not that we're just not seeing the kids), then comes the story about how we need to take them that day because, she can't find a sitter, she needs to work, if we don't, we're taking food out of the kid's mouths, she can't afford to get them nice things, need to pay her more child support to offset her loss of income, etc etc. Probably in there she'll work in a jab about "it must be so nice to have time that you can do the things you want, I never get time to myself because I have to work all the time" or "it must be nice to go on trips because I'm too poor to afford to do nice things like that for our boys" despite the fact that she works about 20 hours a week and my husband works 2 jobs at 60 hours per week and I work 2 jobs at 40-50 hours a week... And she's going to Disney for 10 days in a week with the kids and she bought them Kindle Fire's for Christmas (they're 4 and 6). When we point out how much we work vs her and how the kids are still getting nice things, and that she gets two entire overnights per week with no kids whereas we never have overnights without any children, she says that her schedule is none of our business and she doesn't care about what we're doing. And on and on it goes until she cusses us out and we go with a medium of her schedule and ours, with the threat that "next time" she'll not compromise, take us to court, demand more money, etc etc.
And that's pretty much how setting the schedule to see the kids plays out for us. Every. Single. Month. And while I'm an equal parent to the kids by my husband's treatment of me, I'm not by her. If we can't take the kids because I have something going on, she "doesn't give a *%$" about my schedule, the kids are between her and my husband. I made a photobook for one of my stepsons, she threw it away. Just this weekend at a work party, the kids came over gave me hugs, and sat near us to eat dinner, and she responded by being thoroughly nasty to me, gossiping about my weight within earshot, and otherwise being completely rude. Though when the kids were sick and needed to be picked up from school, she just couldn't miss work, but asked my husband to send me to get them and asked why I couldn't call out.
As one can guess, that gets exhausting for us. At first, my husband used to get these tantrums for her and come back to me and ask if I could change my schedule so that we could go with hers and skip the fight. Then that lead to issues as I was starting to feel like every month, I'd set my schedule, but I'd have to undo it to accommodate hers. I felt like the priority in our relationship when it came to allotting time was his job took priority, her wants/job schedule took second priority, and then I was left to piece together the rest of it after she had her say. But good communication, me coming to him and saying that it's not right I'm changing my vacation dates to accommodate his ex-wife's work schedule, and him taking a stand and being strong in her behavior... The problem for us was over.
You can see in the latter situation with us, it's very different than the first situation with my father to be a step parent. My Dad was regarded a full equal by all parties, I'm not. The relationship he had was cordial, ours is adversarial. That plays a huge role in if this kind of dynamic works. There were plenty of times where the stress that was caused specifically by her was so much that we both questioned the relationship and if it was worth it. But once we made that jump, we took the him and I as a team mentality and we fight it out to make sure we see the kids, but also so she doesn't act like proxy wife who rules our household.
Will the differing value system of the other home compromise the parenting of this child, or any future children they have together?
It will only if the other parent allows it to be, or you allow it to be. Be prepared to hear "well at my other house, I can do X" or "my Dad/Mom lets me do Y" as a response to being told no... And it may be true or not. If you have solid, consistent rules at your house, where they know what to expect, even if it's different from the other household, you'll still hear it, but it won't be a huge drama. It was never an issue for my sister, and it's rarely an issue for us. And the children act very, very differently for us than the do for her.
Will it impact the children they have together? If the other kids have the same rules as their joint child, then no, not really. The conduct of the other household won't impact them that much at all. If they have different rules, then yes, there will be issues. A biological child will resent you if you're more lenient with the stepkids, the stepkids will resent you if they perceive you're more lenient with the biological child. So equal treatment is a must. The rules the biological kid follow full time have to be the same that the steps follow part time, without exception.
The only thing that rubs off is that the kids, especially the oldest, act differently with her than us, and he tries a lot of stuff with us that he gets away with in her house. So, for example, if he's sent to time out, he used to sack the place, throw stuff, scream and shriek, etc etc. The youngest (ours) started copying this. Since it's unacceptable behavior, neither are allowed to get away with it, but because the oldest does it and gets a reaction with Mom, he tries it here, and those attempts get repeated with us. Now he doesn't do it with us at all, but with her, he still does it all the time.
Does the transition happen naturally at this child's age (under these circumstances), as far as a parent-stepchild bond, or not really?
Yes and no. It all depends. It depends on the step, it depends on the adult. But either way, natural or not, it's something that one has to work at maintaining, building and growing it. I'd say a degree of it is natural, but to cultivate it to a point of parent/child, that part takes work. If there's no natural bond, trying to make one will be hard.
And how does a person cope peacefully with their spouse's co-parenting arrangement?
See above.
Sometimes the only peace the situation affords is knowing there never will be peace, but knowing that you guys are still operating in the lack of peace as a unit.
Does that mean when it's time to decide our schedule I don't get a pit in my stomach when I hear he gets a text and know it's her "round 1" of an argument? No... But it means that I know my husband won't give the inch that leads to the mile that causes us to ask why our time and relationship and when we can be together or do things is dictated by his ex wife's demands. I know he's going to run things by me and we'll talk and compromise first between us, not he'll compromise with her and try to explain it to me.
I would GLADLY spare other people the hard lessons we had to learn. Looking back, we had no idea of the difficulties ahead of us, and we've had to crawl tooth and nail through it. 
