my mother has not had a sponge bath since i do not know when, we had a brand new wheelchair accessible shower installed and she just keeps making excuses about why she can not use it or how she will give her self a bath? she can not get to sink so i do know why she is refusing. i think her belly button and under her breast are raw again?
As for using the bathtub/shower, I know some people have a fear of falling. Even I did when I was younger, I found a really nice white Rubber Maid bathtub safety mats [unfortunately they aren't as easy to find now a days].
After my sister died from all of the stress mother put on her, Mother went to the hospital - rehab - assisted living - and the NH. Guess what? Suddenly she is dressed, clean, has her nails and hair done, etc. Every patient there is clean and dressed.
So, sometimes keeping them at home, is not actually the best route to go. Mother is 95 and fine. My sister wasted a good portion of her life jumping through hoops for Mother. (Good luck, to you. Every case is different, but the same in many ways.)
Caring for my 90-something parents I have developed greater tolerance for the folks at nursing homes. Caring for the elderly is much harder than caring for infants and toddlers, because you need their cooperation to do most things. They can be just as ornery and stubborn as toddlers, but they're not portable.