My first thought is wouldn't any licensing authority require a wheelchair accessable shower/bathroom?

Is the lower unit much more accommodating to your child in a wheelchair? 

Consider a service dog like you would consider a wheelchair -- would you not allow a tenant's guest to use a wheelchair?

All but one of these is usually visible and apparent on your first meeting, i.e. a landlord could assume an applicant wearing a hijab is of the Muslim faith, or someone of darker skin tone is of ethnic descent, or a person who walks with a cane or is wheelchair-bound has a disability, or a person who speaks Spanish fluently (or conversely doesn't speak English well) is of Hispanic or Latin or non-American descent, or a woman is, well, a woman.

You don't ask a blind person, or someone in a wheelchair if they are disabled.  

That would be the only occupancy limitation for residences for any group protected under the ADA, other than special needs categories (wheel chair access, etc.).The whole point of this is to protect the disabled (in this case prior addicts / alcoholics) from being pushed out of a community through unfair ordinances, simply because the community doesn't want them there.  

The only benefit I get where I live, is that the landlord can't charge me a pet deposit, because my dog is equal to a medical device, like a wheelchair - she's not legally a "pet."  

If they are obviously disabled, such as blind or in a wheelchair, or on disability income, you can't ask them to prove they are disabled, either.But, you can ask them to provide proof from their legitimate medical provider that they meet the criteria for a disabled person, regarding reasonable accommodations.  

I have been told that if you wouldn't charge more for someone in a wheelchair, you can't charge more for someone with a service animal. 

You could apply the same matters of running an efficient operation to having to take time out to oversee a ramp being set for wheelchair access, putting in grab bars in a shower or removing lower cabinet doors in making reasonable accommodations.