Shes told you what the problem is, she misses her dad. Dont think you should look for an alternative explanation as that ones perfectly plausible and by looking for something else your likely to create a problem that actually was never there.

I think her dad has been a bit soft about it and should do more to ensure mum and daughter have a positive relationship and not allow the 'stamp feet and get my own way' behaviour but if she's happiest living with dad perhaps its time her parents considered making it a full time arrangement.

This is all just personal beliefs so dont be offended with my opinion.
Maybe she feels threatend that her Dad has somenone new in his life and she lashes out at her Mum as she knows her and what buttons to push as well.
It could be that she views coming over to her Dads as a treat as he isn't going to do all the boring homework/chores/discipline etc as he only has her for wknd and when she goes home she lashes out at her mother who may have stronger house rules. You would have to ask her and the mother what they've said to each other and maybe this would give an answer.
Either the Father has to be more disciplined or the mother less, but not have one house seen as the"fun house" and the other as the"boring/mean house"