I am moving back in the hope that she will see changes in me
No. If ANYTHING you do related to DB is for her, it will backfire. You are moving back in because YOU are the one who hopes to save the M and the marital home. You are a decisive leader who stands up for what is right. If not for you, then for your children. You are a man of integrity and honor who shows his children the way to face adversity with strength.
She wants to leave? Fine. Open the cage door and set her free. But you CANNOT "nice" her back. Drop your expectations. The way to look at it now is to identify what would make things worse, and then avoid doing that.
And I'm sorry to have to be one of the first people to mention this, but it applies to almost everyone here: consider the strong possibility that there is an outside party involved. If that is something you can't handle, decide now how you want to proceed.
H: 35 W: 33 M: 11 T: 13
4/10/18: I discovered A and confronted ("BD1") 6/23/18: I moved out 8/31/18: MC ends ("BD2")