I would also have some of that criteria placed in your ad as well as stapled to the application when the PM is handing it out to the applicants at your property showings. 

Assistance animals are not protected under the ADA.

This is probably an ADA topic.

Just don't violate ADA on this one. ..don't ask what her disability is, etc.  

Yes.Am I allowed to demand proof, without violating ADA?

We also print our mission statement in our ad as well: "We strive to provide safe, clean, affordable, comfortable and quiet housing for responsible renters in the neighborhoods of west Vancouver."

An ADA violation could turn out to be much more expensive than the damage a pet could contribute. 

When you buy them you can see if they are ADA compliant.

We routinely offer to change out toilets to chair height (also known as ADA height).

You have every right to require her to prove she has a disability, under this act, that requires a service dog.You would be required to allow a service dog, to someone who is disabled under the ADA, if they asked for a reasonable accommodation for their disability.