For tax purposes, a parent may only claim a dependent if the dependent meets the criteria of "Qualifying Child". Under part three of this, your daughter would need to live with her father for the majority of the year in order to be claimed on his taxes. If this is true, it shouldn't be a problem to file taxes and FAFSA this way. However, If she lived with you for the majority of the year, you should be the one to claim her on both the FAFSA and on your taxes.
For more information on claiming qualifying dependents, see http://www.irs.gov/publications/p504/ar ... 1000273723
As far as FAFSA goes, the parent information used needs to be from whomever the child lives with at least 50% of the year. If it's equal, the parent who provided the majority of financial support should provide their info.
I hope this clarifies things a little. When filing FAFSA and taxes, you should always make sure you're doing it correctly, otherwise there could be flags when matching up IRS and FAFSA data. Doing it right the first time will save you a headache down the road.