M.
My daughter was like this and still is to some degree. It was in part my fault because for the first year or so, I really wanted to "do" everything. By the time I was ready to let my husband help, she wanted nothing to do with him. We went through some very rough times in our marriage because of it. the daycare drop of was the same as you are explaining, even when she was three she would still cry somedays.
When I was not around, she had no issue with her dad, so we started having him take her out of the house to the park or something. She would not be happy about it, but once they left all was well.
I would also have him read books to her at night (with me in the room). I would have him play barbies with us (with me in the room).
All of this was very hard on him because he really thought she hated him, so it made him want to back away at times. But he hung in there.
I dont know your situation, but when we had our second baby (she was four) it helped emensely. I think a big part of it was I had to let go of some of the control and allow my husband to do things. She also had to start relying on him for things which built up thier relationship a lot. She still prefers me, she still cries when I leave, but she also has bonded with her dad and looks to him for things I cant give her (he is much more senstive than me :)).