I'm sorry to hear what you are going through. I know it must be very VERY hard on your D as well as you. My dad had multiple affairs and even 2 kids while married to my mother. I know at her age mine had already divorced (they divorced when I was 13) but I know the pain and she feels. I would go through cycles of hating-loving him at that age. I would want to spend time with him but then knowing how bad he was hurting my mom made me hurt and want to go home. I think its good you want her to do something for his birthday but I wouldnt force it.
Just know that she will truely love and look up to you as being there for her. I know my mom is my rock as I'm going through this and we are very close because of what she went through with my dad.