Legal Question in Consumer Law in Texas

The creditor (whether you refinance or don't refinance) doesn't care where the payments come from each month, as long as they receive them on time.

Any transfer of ownership (her interest) in the car would, of course, still be subject to the seller's lien.

The title can't be transferred to you until it's "clear" - after the creditor releases its lien.

A motor vehicle in Texas is owned by the person whose name is on the title.

Conceivably, she could sign some sort of document purporting to sell you the car NOW even without a proper transfer of title, but there may be a problem enforcing it if, later on, she changes her mind and refuses to sign over the title to you after the car is paid for.