It really isn't easy, especially when you need some time out, so I hope its just a phase. Don't feel guilty that it was somehting you've done or didn't do - it could just be her character - she may just need a bit more security from you at this age to help her grow and become a more confident child when she's older.

Out of curiosity, will your DD play with DH? You might already do this, but I know my DD loves having a play with her dad - he throws her round, tickles her, chases her, etc. And because they have a great time doing stuff together, DH doesn't feel neglected when DD is tired or sick, etc and just wants to cuddle me.
Another idea, not sure if it will work, but is there something that your DD can do with her dad - such as swimming lessons, something they can do one on one without you. DD has been going swimming since she was 6months old, and the majority of the time, DH is the one to get in the pool with her, I've always just sat waiting with the towel on the side.