My mom is dead and when she was alive she basically never showered. Like, I disliked hugging her because she smelled so badly. My brother and I discussed this at length a few times - she claimed she showered when we were at school but we saw no evidence of moved bar of soap or bottles of shampoo/conditioner, no used towels where used towels were put, etc. She literally went decades without showering or washing her hair. I think she would use a wet washcloth to sort of "spot clean" her body sometimes (less than once a week?) and got her hair washed when she'd go to a salon (3-4 times a year).
OP, I know this won't solve everything, but can you get your mom one of these body wipes, and toss any jackets she brings to your house when she stays in the wash for her?
https://www.tbqtalks.com/top-five-body-wipes-to-use-when-you-cant-take-a-shower/