I'm sorry you are in this situation. But please take some time to read some of the posts on this forum. You will realize that "amicable" is not a word used very often here. If your STBX is cheating-you will not feel amicable for long. I feel pretty sure that the g/f is sending you those emails. I bet she wants him to move out and ASAP-so they can have a life together.

Tell your lawyer everything and do what he/she tells you too. Kick out your STBX. I don't know if you have children together or not-but I would make sure your STBX knows you mean business.

Good luck. Take care of yourself.