I am sorry to hear of your situation! I would not wish this upon anyone. I almost got a divorce at the end of last year (less than 6 mos ago). There was no infedility involved on either side - just a lot of other issues. We ended up deciding to work on things.
First of all, if he leaves, it could be considered abandonment or vice versa. I don't know that you can just get him to leave unless it it by his own choice. If he was abusive to you or the children, that would be another story. I would try to find a good lawyer to start drawing up a separation agreement. That way, finances, child support/custody, and living arrangements, etc. could get figures out asap. In most states you have to have this done first before a final divorce agreement is drawn up. You might want to consider mediation, if you cannot come to some type of agreement. Of course, he would have to agree to go - sometimes not that easy!
I could give you the name of a couple of good lawyers, but I don't know if we live in the same area. I wish you the best of luck. Stay strong and convicted and try your best to think of the children. If you go through a long and drawn out divorce - which will cost you thousands of dollars, ultimately, the only winners here are the lawyers. You and your children will suffer. Try to make this as amicable as possible. That's the best advice I can give you.
Best,
Annie