This is just me, but if your mother can't get around except with a walker or canes, I don't think she should be alone with the dog loose, not even while you shower. I have large dogs, and when I broke an ankle, I rented a wheelchair and used it to get around whenever there was the slightest chance of exuberant dogs accidentally bumping into me in the first weeks of healing, even though I was technically using crutches. It's not that my dogs don't obey me, just that I wasn't willing to risk getting knocked off my feet with a surgically repaired ankle.
I'm older myself. Old bones break easier. Old skin tears easier. So in your shoes, I'd work on teaching the puppy to be respectful and obedient to your mother, but I wouldn't take any chances either. I'd put that young dog in a crate or gated off room any time I couldn't be present to intervene and supervise.