Stop believing him, since he's repeatedly lied to you?
You need to stick to your guns, L&C. If you feel the right thing to do was to ask him to leave, why did you then back down?
For whatever reason, I think it's clear he's addicted to this OW. He needs to decide what he wants to do, but YOU should make it clear that you won't live in an open marriage. I'm assuming that's what your position is?
