I don't think it's so much that she can't stand Daddy. I think she lived through a loss. He deserted her. He disappeared from her world and she missed him. The trouble with kids is that they are too young to have the words to say anything like that, but they can act it out. So perhaps she is angry at him for leaving her and she's punishing him.
When she points to Daddy's pix, you can say something like, "yes, that's Daddy. I missed him when he was gone. Did you miss Daddy when he went away?" She may not know what "missing" means, but maybe you can come up with a better word. And then you can add that you are really glad Daddy came home. And you can tell her he loves her. She'll come around. But she has to deal with her trust issue.
Another thing you can do, when talking about the pictures is to talk about games she played with Daddy. Did they play peek-a-boo ? Stuff like that. Remind her of what she did with him, even if it's in language she can't use to speak. Children can understand a whole lot more than they can verbalize. Talk about how you like getting and giving Daddy hugs. Talk about how Daddy loves her, and loves to play with her. Reaffirm her relationship with Daddy verbally, and remind her that it exists. When she finally reaches back out to him, it'll be as if this never happened (in her mind)
But it also is a reminder that the next time he goes on a business trip, you have to talk about it before it happens. He'll need to tell her he's going to be gone, and that he will miss her and he will come back. Maybe he can call when she's up, so he can talk to her on the phone, so he keeps the relationship going. Obviously she won't talk back, but she can hear his voice and know he still exists and he's still in her world at some level, also that he's coming home And when he's preparing to come home, or en route, you can remind her that Daddy's coming home. You can prepare to do something special to surprise him, and make it fun for him to walk in the door.
Remember that with a young child, when a person leaves, they don't have the understanding that the person is alive somewhere else, the person is smply GONE -- kind of like being dead. As an adult, you see life differently, but if he faked his death, and was gone for 3 days, during which time you really believed him dead, how would YOU behave when he returned ??? Obviously that didn't happen, but think about it, because it will help you to understand her reaction.
the other thing that is really important is for your husband to be very clear that he is the adult in the relationship. That means that he has to be the mature one. He has to allow her the freedom to be the child, acting out her feelings, and to continually reassure her, tell her he loves her, allow her the personal space she seems to want, but also continually reach out and be ready for the moment when the falls back into his arms and plays with him again. This has to be killing him, but he has to remember not to take it out on her, and not to take the present phase as if their relationship will be this way for the rest of their lives. I think it'll cease fairly quickly, and I suspect it'll be an instantaneous thing.
hang in. If kids are anything it's unpredictable and challenging. But you guys will get through this, and things will return to normal. And when it does, you may find that you are relieved on the one hand, and a little disgruntled on the other, because she'll be wanting Daddy instead of Mom !! :-)