My daughter (18 months) is the same, if she sees me, she doesn't want anyone else, the second person is her daycare provider, then her dad. The day before yesterday, when my husband went to pick her up, she held onto her daycare provider and didn't want to go with dad, dad was crushed...
It is actually healthy and important that she established the security attachment with her daycare provider because she spends most of her day time there. Also, for girls, before 2.5 years old, she identify herself the same as the mom and female caregiver and it is natural for her to be closer to mom and caregiver (there are exceptions, but majority are this case), between age 2.5 and 5, when she starts to get attracted by the opposit sex she will want dad for everything. My husband always tells me "one more year to go she will be dad's girl and dad's girl only!" of course he is joking (try to make himself not feel so bad).
Your husband's case... is difficult on you and your daughter and you can not change one person, but you can influence him, try to tell him it's the case for other girls too and it is temporary. Your kids are so young and it is important for you to be happy and be able to focus your energy on taking care of them. If you could (I know it's hard!!), enhancing the relationship with your spouse is the best gift you can ever give to your children. A not-so-great dad is way better than having no dad.