Falls frequently, as a result has sustained serious back injury. No longer able to walk without assistance. Has severe pain. Refuses to accept that changes are needed such as the use of an electric skooter, rearranging of furniture in her house, need of constant supervision to avoid another fall.
The person with paraplegia due to a spinal cord injury who stays in bed because there is going to be a cure and they don't want to get used to using a wheelchair is pathological; the one who insists daily they are going to walk out of the hospital but participates fully in rehab is adaptive. What you want to do is create a face-saving route from pathological to adaptive; you may make some headway by treating the changes as if they were temporary things, (i.e. Mom, I'm gong to move this wastebasket over here just until your back is better to make sure you wil have more room to walk") or just provdie some things as a matter of course like arranging for someone to be there all the time rather than asking her to "accept" full time supervision.
No guarantees anything you try will actually work, of course. My mom did pretty much the same thing. Sadly, my rearranging of the furniture, that she did not want me to do, did not help, because she never did get back home again. She could have been home using a wheelchair and some home health supports, but she only wanted to be home if she could have been home by herself, and walking, which was never going to happen. She would never use a scooter - probably afraid to try it - and became more or less immobile in the manual wheelchair. She was good about using her walker and let them put in a few handrails, which is what let her stay at home as long as she did.