The maximum credit for a dependent over age 16 is $500. And unfortunately, you are not eligible for any of the college tuition credits from your child's tuition because those credits are disallowed for the married filing separate status. (This is part of the law as Congress passed it, I don't know why.)
However, the intangible benefits of separating your finances are probably worth the money you would have gotten from the tuition credit.
In the case where the child can be claimed as a dependent, but the parent choses not to claim the child, the child can claim the tuition credits on their own tax return. However, the credit can only be used to negate a tax bill, it can't be refunded if the child owes no tax. If your child has more than about $20,000 of income, it may be the case that if you (a) filed an amended return to remove your child and pay back the $500, and (b) your child filed an amended return to claim the credit, they might get more in credit than you have to pay back. But the only way to know is to test it, and this only has a chance of working if the child's income is at least $20,000.
