It isn't clear from this description that your mother has Parkinson's disease, but you're wise to encourage her to have a doctor evaluate her symptoms. Your mom's reluctance to see
a physician could mean that she suspects something is wrong, but she's not ready to deal with it yet.
If the problem is Parkinson's disease, unfortunately it will get worse and at some point require medical attention. In the meantime, if she absolutely won't go to the doctor, then I think you have to respect that. You may find this difficult, but parents are adults, not minors. You can subtly keep coming back to the issue, though. If you keep saying, "I think there are some really good medicines for the symptoms that you're having, Mom," sooner or later, she may want to feel better, and that could motivate her enough to get an evaluation. Or sometimes a person will be more likely to listen if another family member offers the suggestion.
In my experience, you can usually get an older person to consult her regular doctor who she's seen over the years for a routine health matter. For example, you could say, "You know, Mom, they've got the new shingles vaccine out. I would really hate for you to get shingles."
So you might convince your parent to make a medical appointment without focusing the entire visit on this one concern about Parkinson's disease. Then, if she'll let you accompany her to see the doctor, that's a good thing to do. If Mom doesn't mention her shaking foot, you can bring it up.
But if she won't let you into the exam room with her, you can still accompany her to the appointment and wait outside. When the reception desk staff initially takes her information, you might mention that you have some concerns and ask if it's possible to speak with the doctor or nurse for a minute before the appointment.
Alternatively, you could call the doctor after the visit, but he won't be able to discuss your mother's situation unless she has signed a statement authorizing the clinic to share her medical information with you. So see if she'll put your name on the "OK to discuss with" list at the time of the office visit.