@ThaGuy,
Gadzooks, you're married to a selfish bitch.
Seriously, she has decided on 100% of how things are going to be.
Please don't stay together for the sake of your children. You'll be teaching them a big-time lesson about how love is a lie and marriage is for saving money and for children only and not for the adults.
Your wife wants to have her cake, and eat it, too. She wants to string you along forever while she fucks other guys. Sorry for the vulgarity, but seriously, this is exactly what she is proposing.
It would not surprise me if you were also expected to continue to work and pay bills, and also watch the kids while she humps anything in slacks.
Please consult with a divorce attorney. You have rights. Your children will be fine; they are more resilient than you fear, and yes, unless they are very tiny infants or they are profoundly disabled, they
know there is something going on and they
know you two are lying to them when you pretend everything is wonderful.
I don't think this trainwreck can be saved. And, I might add, get some counseling and figure out why you would allow yourself to be abused (yes, that's what this is) like this by someone who doesn't give a damn about your feelings.