I ask my wife why she wants to stay married to me and her response is because she loves our family. I interpret this to mean she doesn't want our kids to grow up with divorced parents. On one hand I suppose this gives our marriage some much needed stability, but on the other it's kind of insulting to me. she had the affair and the only thing keeping us together is her fear of what this will do to the kids? I don't want to leave my children, but I also don't want to be in a loveless marriage.
Tough one but might not last if she isn't willing to work hard at rebuilding your marriage first and foremost. This might buy some time for her to come around but in the end your marriage needs to be number one next to God if you are going to have a healthy home for your kids. My wife grew up never seeing her parents show love and it has added to her many messed up problems.
If you agree and understand not wanting to split up the kids, then keep trying to do things to bring the love back around. Date nights, dinners, etc. That's if you can get over what she did and if she's over it as well. Seems the cheater needs time to get over what they did as well I'm learning....which is complete bs but it is what it is I guess.
I am often afraid that my husband is only staying b/c of the kids. I ask what he wants and his answer is "Our Family." Well... yeah... but he can have his family without me. Our kids will still be HIS kids if we aren't together. It's painful. I know he loves me and the kids... but is this only for the family or does he really want US as a couple.
I feel your pain. Be strong.