Person who I claim as a dependent but doesn’t live with us (court ordered-dependent) is now being paid by us to watch younger sister can I claim the child tax credit for the money paid to her?

No.   You are asking about the childcare credit (not the child tax credit).     You cannot enter the child and dependent care credit if your childcare provider is claimed as a dependent on your tax return; whether that dependent lives with you is irrelevant.

You can't claim the child care credit if the care provider is also your dependent.