I don't see anything in the FAFSA that asks about dependents of the parent. Are you referring to the question that says "How many people are in your parents' household?" The instructions in the question tell you exactly who to count. It's not the same as dependents on the parent's tax return, and it doesn't use the word "dependent." According to the instructions, the student always counts, even if she doesn't live with the parent.
If your daughter spent more time at your ex-wife's home than at yours, you cannot claim your daughter as a dependent on your tax return unless your ex-wife gives you a signed Form 8332 allowing you to claim your daughter. Dependents on your tax return are determined by tax law, not by your divorce decree or any informal agreement. There is no such thing as shared custody in the tax law. The custodial parent is the one that the child lived with for the greater number of nights during the year. You can only claim your daughter as a dependent on your tax return if she lived with you for more nights during the year than she lived with your ex-wife, unless you have a signed Form 8332 from your ex.
