I called Priceline today not expecting them to do anything. To my great surprise, they canceled my reservation without much hassle at all. I did not quite get what the person was trying to say. It seems like there is a law regarding this kind of situation. I had to provide the doctor's name and contact information. He took the information and told me another department will verify the information. I received the confirmation email shortly.

They deducted $100 cancellation fee. But I can get $70 back if I book another ticket for my Mom. It turned out to be much nicer than booking directly with United.