I'm sorry about your daughter struggling so much. I am very grateful that my kids don't know about their father being so dishonorable. In some ways it is easier for them at this stage, because they see his apartment as more of an adventure than a desertion. I'm wondering how long it will feel that way.
As far as deciding if the A is a deal-breaker, I would suggest giving it some time. My H gave me a lot of apologies, etc., too, but in the end he can't seem to turn his back on her. So don't feel like you have to make a decision how you feel now. You may not yet have all the facts. Marriage counseling might help with that, if you can see that he is using it to make an honest effort.
Hugs to you...
Me42, H40 D12, S8, S7 A revealed: 7/13 Sep 4/14; Agreed to D 1/15