Can I claim my daughter if our court order states he must have all payments to me for the tax year to be able to claim and he doesn’t?

This is a legal question, not a tax question. Ask your lawyer if it's okay for you to claim your daughter as a dependent.

If your lawyer says you can claim your daughter, it might be a good idea for your lawyer to formally notify the father that he is not allowed to claim her this year. If that discourages him from trying to claim her, it will save you the trouble you would have if you both claim her.