I mostly agree with NapQueen. DD is both yours and your DH's responsibility.
Now, I also do know it is hard and very upsetting when your child seems to hate you. Hate is a strong word, but DD really, really, really disliked being with her Dad (at least when I wasn' there). In fact it is the emotional side of this behaviour that is extremely draining. People who've never had high needs kids or whatever you want to call them cannot possibly understand.
My DH was upset about this, but eventually learned to live with it and give her time/space when needed. He also learned (or perhaps I taught him ) that it was equally distressing for me. We are both her parents, the burden of any practical action and any emotional stress MUST be born by both partners equally.
You must be firm on this, or it will really drive a wedge between you. Don't let him get away with not pulling his weight. It's just as hard for you as it is for him.
Do reassure him that it will pass, and the more contact and patience he has with her, the sooner she'll come round to it.
To this day we have no idea what it was that made DD have such extreme reactions to being left with her dad. But he gritted his teeth, was as patient as possible with her and that loooong, horrid phase did pass. But he didn't give up on it. And I didn't let him give up.