Is it permissible to obey one's mother in registering her at the doctor's and letting her go alone?

Obeying the mother is legislated in her request for you to register her with the doctor. The fact that she will go alone does not prevent you from registering her. However, if the doctor's appointment will involve khalwa (private seclusion), then you must explain to her that this is impermissible. She should go with someone who removes the khalwa, if a mahram (unmarriageable kin) is not available.