I hope those links Aineo gave you are helpful.
Are both of you Christians?
I admire your willingness to stick with your marriage commitment.
There are a few things I'd say should be thought about though.
One biggie is that this is something you need to make HER think about. It sounds like she has free rent, child care, and spending money with you, while not having much obligation to give you anything in return, not even sex. I'm gonna bet she realizes that, but point it out anyhow if you haven't already, and ask her if she really thinks it's not that bad of her to ask you to continue the marriage and if her intentions are truly to keep the family together, or because she realizes she has it made in this situation. Especially when she's given you biblical grounds for divorce. Regardless of who she is unfaithful with, it's still unfaithfulness, adultery.
Believe it or not your kids will figure it out sooner or later, and either learn from your examples or turn against you. Both of you have an obligation to ensure that those kids are healthy and properly fed, both physically, mentally, and spiritually.
I truly hope both of you find a way to work this out. I believe ANY marriage CAN be saved, but in this case it's going to require quite a bit of commitment from both of you, and a lot of talking and decisions.
Chrys