I know this isn't what you asked for but hugs.
You can try to use "that won't be possible" but it might not work or you might just get it back with a trump " that would be possible." with unspoken "and she doesn't live here anymore and you can't make me, so either take her yourself or watch_____(whatever the repercussion of not going to the doctor)."
I would start looking into other options. Talk to lawyers , accountants , churches , the county/state/city services offices , every charity you can think of. They have sources and information that many people don't and may be able to help even with finding transportation or money you/your friend is entitled to off set the cost of a helper.
Now I think you could rip into her mother a little and have it still be polite she dumped, in a horrible dehumanizing humiliating way, her daughter on you. I'm getting the impression it has been some time that your friend has lived with you. I think you could publicly shame her. "How's Itchy Mom ?I haven't seen Itchy Mom in a month we used to chat every week when she'd come to my house to talk her daughter to the doctors, you know her daughter has been living me since____, but she hasn't been doing that anymore. So I haven't have a chance to talk to her."