You've gotten a ton of responses and some great advice. My husband and I just went through all of this. We have a 3 year old "mommy's girl" and now a new 8-week old daughter, too. We made a concerted effort to get rid of the mommyitis by doing several things:
1. I holler "Daddy's home" when he gets home at night. I act very excited to see him and it carries over to her.
2. I encourage her to be nice to Daddy and when she is downright ugly to him, she goes in time out or gets a swat on her bottom from me (and only me). I wasn't sure about the punishment side of this (like I was forcing her affections for him), but my husband and a friend of his were talking and he and his wife had had this problem with their daughter. They had to do this a few times and it resolved. We had the same experience. After about 3-4 "punishments" for being outright ugly to her dad, she very very rarely does it now.
3. The two of them need to spend time alone. Going somewhere together is important but it is just as important that he be the one to take care of her at home so she knows she can rely on him to do all those things that you do for her. I also reinforce this by telling my daughter that Daddy can do those things Mommy does just as well, and sometimes better, than Mommy.
4. I encourage her to love on Daddy - crawl in bed and give him a good morning hug before he gets out of bed, give him a hug when he gets home, etc. If she doesn't or balks at doing it, then I hug him and we invite her to come hug both of us. Then she is pretty easy to pass off to him for "Daddy bear hugs."
5. At first, we had to have my husband start putting her to bed every night and she had to cry out any upset over that. It was really hard to stay out of her bedroom and let her cry. Eventually, only after she would go to bed for Daddy without any drama, my husband and I started taking "turns." It is Daddy's turn to give her a bath or tuck her in. Mommy has a turn the next day. Most of the time she forgets who did it the night before so he does it more often than I do just to reinforce that bond they are developing.
6. I told her before the baby came that she needed to help me take care of Daddy by letting Daddy help her more. She seemed very responsive to that.
7. We refer to the baby as "our" baby and encourage her to help out so she doesn't feel left out. We take turns with the girls so she doesn't think that the baby is getting all of my attention. That seems to help with the mommyitis as well.
8. My husband does the grocery shopping about as much or more than I do. I will tell our daughter that he bought her something special at the store just for her - popsicles, Toaster Strudel, whatever - and he did it because he knew she would like it, Daddy did something nice for her, etc. so she understands that he thinks of her and wants her to be happy. She makes that connection.
9. I made up new words to Frere Jacques (Brother John): We love Daddy, We love Daddy, yes we do, yes we do, Daddy is the Greatest, Daddy is the Greatest, yes he is, yes he is. It embarrases my husband, but we would sing it and sometimes I catch her singing it when she is singing to herself. I would sing it to her just when I thought Daddy needed some boostering with her. It's silly, I know, but it seems to help.
10. I even told her she had mommyitis and that we were trying to make it go away. I told her that mommyitis made Daddy sad because he wanted to be able to do things for her, spend time with her, etc.
11. I've told her that being ugly to Daddy makes me sad because I picked him special just for her to be her daddy. She really listens when I tell her this and seems to take it to heart.
I don't think it was just one thing for her that helped the problem. Now, it is very rare that she is ugly to him or clings to me over him. She fell down last night and went straight to him to comfort her instead of coming to me. I know that we are on the right track.
Good luck! It will be fine.