H.B.
J.,
This is entirely normal! Don't worry too much. I know you mentioned that most little girls her age will run to Daddy happily, but I really think you are just noticing the ones that do....and not noticing many still do not :-) Children with a stay at home parent often have a closer relationship with the parent that spends the most time with them and provides more of their daily care and needs. It is GREAT that he is taking over lots of the evening care-taking. Even diaper changing,bathing and picking out PJ's together will help her see that he is there to take care of her too! Reassure Daddy that this is normal and natural, and you take that stance too....she will certainly bond with Daddy over time, but may do so at her own pace. Have Daddy do LOTS of fun things with her (and with the 2 of you together) to promote a good relationship, but don't force the issue or show signs of being upset over her behavior- or it may get worse or slow... Whoever she chooses to cuddle with, be held by, hold hands with etc should be respected so she develops a sense of trust and security...which will only help with her with every relationship!
In time things will change as everything does with a baby/toddler. I'm a SAHM and my daughter was a total mommy's girl...now at almost 3 she constantly talks about how she's waiting for Daddy to get home to go for a walk, take her to the local pool, go to Publix for a cookie, etc. When I ask her if she wants me to take her she simply says 'no, I need to go with my daddy...' It's hard to believe it's the same girl that used to scream and run when he tried to hug her....
Hang in there and just go with the flow!