The problem with the whole "if we're going to have a relationship you have to think of my kids just like they were yours" is:
1.It's unrealistic: your own flesh and blood is always different than someone elses. These biological attachments are a deep seated part of the human pysche that predate history itself.
2.Can be seen by the children as an attempt to replace their real parent, and will probably be rejected.
So I'm just saying recongize your new adult relationship as being your relationship. Yes, it's going to effect the children, but there's no need to force any degree of relationship on them they don't want beyond the general respect they should have for all people. If something deeper develops on its own, then great. If not, well it's a handy lesson that in life sometimes we have to deal with situations and people we may not like. But you can't grab the kids and say "hey, I'm marrying this guy and he's your new dad" and really believe they're going to just go with it. I'd even say trying that approach ensures failure because it inspires the kids to defy you for the sake of it.