Does she claim to be a believer in Jesus? Have you shown her in the Bible where it says that he who divorces his wife and marries another commits adultery, and that he that marries her that is divorced commits adultery? The Bible also says that a wife should not depart form her husband.
If she's a believer, you should be teaching her the word of God on this sort of stuff. Whether she's a believer or not, I don't think the right approach is to passively 'leave my problem to God.' Of course, you should cast all your cares on Him, because He cares for you. You should trust in Him to work. But he has also given you responsibilities. The Old Testament sin says not to despise your neighbor in your heart. But rebuke your neighbor frankly so that you do not share in his sin. The Bible tells us to exhort and admonish one another. If you are a Christian husband, you are supposed to seek to rule your house well. Having a wife that goes on dates to find boyfriends while you sit passively by and do nothing isn't ruling your house well.
If she talks about wanting to see other people, call it what it is. Whether she is a believer or not, tell her you want stand for any adultery in the marriage. She needs to grow up and take on the responsibilities of being a wife and mother. It may be a bit of a shock for her to deal with all these responsibilities. She may be rewriting the story of your relationship in her mind. Tell her she's made some decisions, and now she needs to be an adult and follow through with her responsibilities and be responsible enough to work on improving her marriage. Do you know what kind of disadvantage divorce is for the kids on so many metrics they measure for children? Giving a child a stable, two parent home is a real blessing to a child. Point this out for her.
You can't let yourself be pushed around by her desires to date or have inappropriate relationships with others. A loving husband will want to make his wife happy, but sometimes it isn't loving to give in to whatever she wants. She should definitely know you won't stand for this sort of thing. She may actually feel safer and appreciate you more if she knows she can't push you around with something so destructive and completely unreasonable. If you let her have boyfriends without 'smacking down' that idea, it may not seem to her like you love her very much. This is a time where you can offer some moral leadership. Tell her you two are going to work on your own relationship, and you aren't going to stand for any of this adultery talk, or especially her committing adultery or having emotional affairs. If she's a believer, explain to her how she's wanting to head down a sinful, destructive path. If she's not, oppose all this kind of talk. You shouldn't tolerate that kind of attitude in a marriage.