How do I convince my mother that it is time to use a walker?

Who treats her Parkinson's? From what I read, one of the symptoms is that ones feet feel stuck to the floor and balance is an issue. I have an aunt with advanced Parkinson's and she doesn't use a walker. But her daughter tells me that Parkinson's manifests differently in different people. A few things come to mind. One, send a note to the cardiologist ahead of his seeing your mom outlining what your concerns are.
Ask him to order PT so she can be evaluated. PT can strengthen her muscles, address her knee and recommend a walker or cane if needed. The therapy might help the ankles as well. My aunt uses a cane very effectively. My mother used a walker. Therapy helped them be more aware of the proper usage and how the aid of a walker or cane could help. She can get the therapy in her home or at a therapy location. Either will improve her balance and walking.
My aunts daughter takes her for boxing therapy to help her Parkinson's. 

Falls are the worst.They can change everything in a heartbeat.Maybe something has scared your Mom like her knee giving out with no warning or maybe she has already fallen and didn't tell anyone.I'm sure she feels safe with your hand to hold.She is lucky to have you and your care for her.I hope you can convince her somehow that a fall,just one fall can do ALOT of damage.Take care~

Well BarbBrooklyn, I tried to get her to a geriatric doctor for an initial visit since she just moved near me, and she was so nasty to the doctor, that the doctor told her that she wasn't obligated to take her as a patient. She's adamant that all she wants to see is a cardiologist, and even that was met with an "Oh no!" when I told her the appt. was tomorrow. The geriatric doctor did look at her ears because I told her she was losing her hearing, and it turned out they were blocked with wax. She prescribed some drops for them then had her come in to remove the wax. She also refused to have a blood test or another appt. for a checkup. Well lo and behold, about 3 weeks ago she asked how I knew she didn't need hearing aids and that her ears were clogged, and I told her it was the geriatric Doctor that saw it. She just smirked. My mom is going to be tough going when it comes to medical care and listening to me for anything! I hope the cardiologist at least says something.

CTT, totally off topic, but some family members and mom's doctor all thought she needed "social support" and "this is stuff mom is doing to herself".

We got mom into Independent Living, where she saw a geriatric psychiatrist on a regular basis to manage her anxiety. Psychiatrist insisted that mom have neurocognitive testing (mom was "sharp as a tack" as far as family could see).

Mom was diagnosed with Mild Cognitive Impairment. The MCI (and the attendant anxiety) was the result of a stroke, seen on brain imaging, but never diagnosed in the past. Big wake up call for all of us.

My mother used to have magical thinking in that her impaired walking Post Answer
ability was only temporary. And that (as she tells everyone) it's "all in my head!" She prefers to walk hanging onto someone's arm when she's out. Didn't want to listen that it was unsafe. No good deed goes unpunished, of course. She says that she can't possibly "impose upon" other people to put her walker in their car, so I'm the one who has to drive her to church most weeks.

The PT was the one who told her she must always have the walker when she leaves her condo. My mother never would have listened to me.

(Oh, and the elevator...does anyone else have the ridiculous scenario I have when my mother encounters an elevator? I must leap into the elevator ahead of her to keep pushing the Door Open button. She panics that the door will shut on her. I also have to hear her admonition to not look down the shaft at the crack (there is nothing to see; it's dark!). Yep...just another of many anxieties and "rules" I must obey...yet her doctor "doesn't like to put older patients on anti-anxiety meds." All she needs is "social support.")

In her condo, she likes to stagger down her hallway with no cane or walker. "See! I'm just fine and don't need anything!"

Someday she will fall, and that will the end of her "independent" life.

I think that's her doctor's job, not yours.

I don't think our parents EVERY start to think of us as "real" adults who might know what's best for them. Whenever there has been something that my mom has needed to be told, we've always been more successful if one of her healthcare providers tells her or if we can arrange for her to think it was her idea.