Having taken care of adults in the hospital who are hygiene challenged, I've come to the conclusion that cleanliness simply doesn't matter to all of us.
You can teach and preach and teach and preach until you collapse, and it changes nothing. We have the same women who are admitted to the hospital over and over with open sores, that simply won't stay clean. Usually, not always, they have low IQs. They're lower income. Their peer groups are people just like themselves.
My daughter is developmentally disabled. Being clean, tidy, and maintaining a socially acceptable appearance doesn't matter to her. We fought and fought. Body wash became the cudgel I beat her over the head with. (figuratively speaking
) She'd wear dirty clothes. Stink up the spare bathroom. And her bed linens absolutely reeked. I did daughter teaching. Bought buckets of hygiene products. Rewarded clean behavior.....
Everything I could think of to encourage her to just stay clean.
Then the light bulb went on in my head. It doesn't matter to her. It's just that simple. She doesn't fear social disapproval and censure. It doesn't bother her that she's looked down on because she smells. SHE JUST DOESN"T CARE. Whatever mechanism that exists that keeps the rest of us within the norms of social behavior, is absent in my daughters head. God help me if she ever has children, because she'd probably be just like the mom the OP describes.
I'm going out on a limb here, but I think I'd let the hygiene issue slide. Not to say I wouldn't teach, teach, teach. You simply can't change another persons core values easily. Maybe the best thing to do is to simply aim your efforts at teaching the children, instead of the mom.