All kids go through this phase. I feel like it is a way of getting a reaction as well as exerting independence. My son at 5 still has "mommy days" and "daddy days" as he calls them where he wants only one of us.
One thing I see a lot of parents do that does not help this though is that they immediately grab the child back when they cry a little or express nervousness. This makes the child feel like they were right to be upset and it continues. You need to make her stay with daddy and just reassure her that daddy loves her and they will have so much fun. Daddy can play her favorite game or sing her favorite song, etc.
If your child is very attached to you, you will need to force the issue. Leave her with daddy while you go out for an hour or go in another room for an hour. You may be surprised that she is perfectly fine when you are not there. I knwo it is hard, but you know she is perfectly safe with her daddy and she will not get used to him being a part of her life if you don't let him take care of her (not saying you do this, just something I've seen other people I know do).
I know some people will probably say I am cruel for saying let her cry a little, but if you take her back everytime you are reinforcing her fear. Give her a little longer each time until she is comfortable.
Good luck.