J.,
If it were me, I'd probably just back off. This stuff happens with kids all the time. Hygiene is often very inconvenient to kids who are busy, and it can sometimes take a comment from a peer to click them into gear. Our love and affection, they want very deeply, and to be told that they are less than appealing can hurt deeply. It may be a struggle that she's so bent on winning to prove a point to herself, and she may not even be aware of it.
You mention that her mother has never taught her about hygiene. This might be worth having your husband speak to your stepdaughter's mom about. (Is there a larger problem at her mother's which social services needs to look into, or is her mom just resigned not to struggle with her daughter?) This little girl may be feeling some affinity to her mom by not complying with your family's requests in this area.
For what it's worth, I don't remember thinking much about this sort of thing when I was a kid. Hygiene was often a rote sort of thing as part of the daily routine. Perhaps offering to sit and spend time with her, to brush her hair and make a routine out of toothbrushing together. Just a thought.
As for the wiping, like I said, I'd let it go. I've taken care of plenty of kids who didn't wipe for a while, for whatever reason, and without adult involvement, the situation always resolved itself. This is her challenge, and if you make it yours, it only takes the focus off her self-care and can potentially create a power struggle.