The ADA and other laws that protect people from housing discrimination due to a disability state that you are not required and it is illegal to ask you what your daughter's disability is when it comes to a reasonable accommodation. They can only verify that your daughter has a disability through a third-party verifier that would have knowledge of her disability and the nexus between the disability and accommodation requested. Never are you or your third-party verifier required to reveal exactly what her disability is. If they ask you, sue them or file a complaint.

I work for a company that has many low income apartment complexes and part of my job is assisting our reasonable accommodation coordinator in making determinations on reasonable accommodations. So, I liason from our home office and individual property managers on reasonable accommodations daily.

"Discrimination against persons with disabilities is prohibited by Section 504 of the Rehabilitation Act of 1973 and Title II of the Americans with Disabilities Act of 1990 (Title II prohibits discrimination on the basis of disability by public entities, whether or not they receive federal financial assistance). This includes discrimination against individuals currently without an impairment that substantially limits of a major life activity, but who have a record of or are regarded as having a disability."
http://www2.ed.gov/about/offices/list/ocr/complaintprocess.html
Key statement is "regarded as having a disability". If you are perceived as having a disability then you are covered too. People can discriminate or treat you differently if you look like you have a disability, even though you may not. I get this all the time when I just run errands without my wig. Hope this helps. Sorry I didn't get to see your post sooner.