Your husband absolutely must go to court and force his ex-wife to share ALL medical information with him. Think about what would happen if the girl were with you and him, and were injured or became very ill -- you will be asked by the ER, "Who is her primary doctor?" and will not be able to answer. You will be asked, "Is she allergic to any medications? Does she have any health history of X, Y or Z?" and you will not be able to answer. If for some reason you must sign her up for a camp or class in summer, you will have to fill out health forms including her doctor's names and numbers, as well as allergies and meds she may be taking; you cannot do that if you do not have that information. Camps and classes and school ALL want immunization dates etc. -- you cannot provide those if you don't have access to all her medical records.
For all your husband and you know, the girl could be under treatment for many things or nothing, or could have developed a life-threatening allergy to a medication or a food etc. and you would have no idea, if the record of all that is with a doctor whom you cannot contact.
I would be very suspicious that the mother has the girl in treatment for something that is being hidden from dad. Possibly the girl is in counseling that was recommended by the doctor and the mom doesn't want the dad knowing or seeing any records. Or the girl could be perfectly fine. But you have zero way to know.
This is very important. It IS worth your time fighting in court over doctor visits. She needs to see the same doctor(s) so she gets consistent care and there are good records of her shots. Dad needs to wake up to this -- he and you could end up accidentally endangering this girl because mom refused to let you have her medical records and access to her real doctors.
If dad pays for any of the daughter's medical insurance -- he needs to know who all the providers are. He should get insurance statements that name her doctors when the insurance pays out or sends him a check -- the medical provider information is always on those statements. Even if he has no insurance responsibility, he simply must know her medical history and providers and be able to take her to HER regular doctor if she is sick when with your family! The mother is negligent to hide the doctor from him -- and she is creating a lot of justifiable suspicion about her motives.
Also, the mom likely has filled out a HIPAA form (which says who can and cannot have access to a patient's health information) and intentionally left dad off that form. He must ensure that he is officially listed as both legally required under HIPAA (it's a health info law) to have full access to information, AND that he is listed as an emergency contact for his daughter. Even if mom doesn't like it.
Involve your lawyer, right now.
The issue with the wiping? Could be as simple as the fact your toilet paper isn't what she's used to. When I inadvertently bought very thin toilet paper recently, I found that everyone was using a lot more of it - a friend of my daughter's sheepishly came and told me she'd clogged our toilet (bless her for telling me right away!) and I saw it was because she'd used a ton of this thin toilet paper. Or your stepdaughter just might be used to the feel of a thicker paper that is at her mom's house. If there is no burning or pain etc. I'd just change papers and let it go. If you favor a particular paper, just keep a thicker one around for when she's with you.