Your daughter has a family. She has you. Sometimes things don’t go as planned and you have to adjust and re/evaluate.
How you react now to this very ugly situation sets the tone for your daughter. If you see set a clear path and figure out how to make things work, then you are showing her that despite life’s challenges— you will show up and survive.
As someone who was about to be D in the blink of an eye (less than 10 days after Dday my H planned to walk out the door for the OW) I knew I was the only one acting with the best interest of my kids at the time. My H was checked out.
While I understand the horrible situation you are going through, it is important that you put the well being of your child first.
That means your lying cheating H needs to be told exactly what is expected of him as a parent. Not in trying to R or salvage the marriage b/c I feel as though you are talking to a brick wall on that front.
But he needs to be present with your child and make up for his not coming home in every way possible.
If he fails, then it’s on him. And you might want to get professional counseling to get help on how to manage this current t situation w/ your daughter. And if her father fails her, you want to be prepared for that situation as well. And know how to talk to her about it so that you don’t cause further confusion to her.
I hope this helps you. I strongly recommend family counseling for you — and when appropriate (if it should happen) for him as well. May not be together right away, but the adults need to put the child first (whether D or R or whatever).