Im not really sure what you are looking for. If you are looking for a specific law that says you can/have to/must give written permission for someone to pick up your child from your ex wife, I doubt you will find it. The laws generally are not written that way.
You might find something like this in the Tn Domestic Relations Code.
Specify that if the driver license of a parent is currently expired, canceled, suspended or revoked or if the parent does not possess a valid driver license for any other reason, the parent shall make acceptable transportation arrangements as may be necessary to protect and ensure the health, safety and welfare of the child when such child is in the custody of such parent
This could obviously and reasonably be interpreted to mean you could send a cab to pick up your kid if your license were suspended or were otherwise unable to drive yourself.
Do you know how to find your states domestic relations code? Everyone getting a divorce should read it at least once.
What, exactly is her argument? That's you and you alone are the only person that can ever pick up the child from her presence? That neither you nor she is ever able to designate someone to pick up the child?
If she denies you your parenting time, the mechanism for enforcement is letters of objection for her failure to comply, reasonable offer for her to make it right and then contempt enforcement or motion to show cause and drag her rear to court.
And don't buy into her framing the argument as a transportation isue on your part. It's not. It's a denial of parenting time on her part. Be sure to frame it as such loud and clear in your letters.