He has never been daddy. He has simply been the man who comes around and brings her gifts and tells her she is cute once every few months. My husband is the one who is her DADDY in all sense of the word, accept the DNA. Her father has began eliminating himself.
First, you have it all wrong or if the world ran your way, every deployed parent or parent working out of town for weeks/months at a time and comes back happy to see their kid and bearing gifts is not "Dad". Your current husband is NOT the father of your child. He is a caretaker that hopefully cares for her, but he is not "Dad". He may even be a father figure in her life, but you can't choose Dad now, she already has the Dad you previously chose.
Don't diminish the role her father has in her life b/c it doesn't fit your picture of a fairy tale. I'm sure it wasn't your daughter's fairy tale to have her 2 parents not be together. She's already a victim of sorts b/c of the adult's actions in her life.
And, it can't be too fun for a dad to watch himself being replaced by your new boyfriend/husband/romance. Do you have any idea how hard it is to be a NCP in the first place? Don't make it harder playing house w/a new daddy and allow her real dad his rightful place EVEN IF it's only every few months bearing gifts. It is what it is and that matters to the child. You can make it sour, but just know that that's your choice to make your child feel unloved if you try to capitalize on the situation to insert hew BF/DH.