I have a question about claiming education credits for my child. If I don’t claim my child as a dependent, but I pay for her tuition, am I still able to claim the education credits?

No. Whoever claims the student as a dependent is the only one who can claim expenses for the credits and deductions. You are not able to claim any education credits for a non-dependent child. To be able to claim education credit, the student in question must be a dependent claimed as an exemption on your tax return.