"Yes, I would like you to move out as soon as possible."
Starting this month, tally up the bills, mortgage, taxes, utilities, you name it and let her know how much she is required to start paying if she continues to live there. Also tally up the time you spend babysitting while she's out bar hopping and living the single life.
She may start to argue, may attempt to make you feel guilty, don't fall for it. You just tell her plain and simple, you made the decision to cheat on me and you want to end the marriage, I'm fine with that, however, you can't continue living here as if we're still married, I plan on getting a roommate to replace you but while you're still here and haven't found an apartment yet, these are the expenses a roommate is expected to pay. I will also no longer be your baby sitter, you will be required to spend the same amount of time that I currently spend with the kids, I won't watch the children 5 nights a week for you. If you have a problem with any of this, too bad, it's just one of the many consequences of cheating on your husband.
And that's that.
"What is best for my kids is best for me"
Persevere = happily being patient over a long period of time