She hasn't come back to you. She came back because for some reason this was convenient for her. I would tell her that until she is ready to come home, be monogamous and work on her marriage she will need to find another place to live.
It isn't fair for you and your sons to get your hopes up. This is your first major hurdle. Stand strong.
kat
This. ^^^^
"I'm sorry, but our home is not a hotel, for you to come and go as you please. It's horribly upsetting and confusing for the kids, and I'm sure we can both agree that we both want to do what's best for them right now."
