My mother is full time caregiver for my 87 year old grandma. My mother is 62. My grandma is very stubborn and will not use a walker, and my mom literally holds her up and helps her walk all over the grocery store, and anywhere else they have to go. My mom's back is in constant pain due to having to hold up my grandma. She is in poor shape herself. My mom has become clinically depressed from years of taking care of my grandmother now and complains to me all the time how she is in pain, but my grandma "is too stubborn" and so mom doesn't even try. I keep telling my mom to put her foot down! Make her use one! But mom just lets my grandma do whatever she wants. My mothers depression and complaining (for 5 years now) is taking a toll on me!
And so many of our elders don't want to use canes or walkers, good heavens someone might think they were old. My Mom didn't want my Dad to use his rolling walker to go to the mailbox, but Dad refused to listen to her, he loved that walker :) No more falls on the driveway.
And there is no need for your grandmother to go along to the grocery story. I finally had to stop bringing my own parents [who are in their 90's] to the grocery store and big box stores.... it was just too much for me.
For groceries I now use an on-line service where I do my grocery shopping and my parents grocery shopping from my own home, comfortably nestled in my office chair. Then the next day the order is ready for pickup or for home delivery. What a life saver that was for me. Otherwise my Mom would have me going every other day to get this or that. That had to stop.
Okay, my answer may be different than many hear, but I think you should concentrate your efforts on mom's technique with the gait belt rather than nagging her to put gram on a wheelchair.
Her mom. Her decision. If gram falls and breaks a hip, there's at least a 50% chance she will die within a year. It took mom nine months. It is such a devastating assault on the body, they aren't even sure why, that it is a deadly injury on someone gram's age. I think gram is actually safer on a gait belt.
In a perfect world, it would be ideal if a physical therapist could meet with both of them to assess gram. If there SHOULD be a switch to a walker, let the PT recommend it. Perhaps you could compromise with mom and convince her to ask gram's doc for a prescription for same. A PT's expertise really could make your mom's life MUCH easier.
I wish you well. AND I compliment you for realizing that one person should not sacrifice themselves in order to care for someone else.
It sounds like this is going to kill your mom if she doesn't get some help. Can you look into getting a home health care aid? Is assited living an option? Mom can "Put her foot down" but that only gets you so far. Sometimes action has to be taken that elders don't like but is for their own good.