Both real estate agents  as well as my wife and I are starting to question her mental health some. 

The offer should also state that any items left in the unit once they move out and receive the money is considered trash.Be mentally ready for the "worst"....as in, it might take longer than you want for them to move.

I knew this would happen eventually, but I still don't know how to overcome it mentally. 

For the mentally ill, If they are really lucky, they have good family support.

If someone in the United States did what you do, they would be subject to a Fair Housing complaint, unless they fit within the size limitation exemption.Neither the codes in the US or Canada state that mentally unbalanced applicants have a right to  preferential treatment.

Maybe is theraputical and their ailing child relies on it as a mental salve?

While figuring out how to get rid of her, if that's what your calm lawyer mental mentor would advise, use the lease.  

It mostly comes down to the area you invest in but sometimes applicants with mental illnesses do get through the process, I know that first hand.

I agree with many who say that the problem may be fairly easy to resolve, but you should check with an expert that does these kind of repairs to confirm if you are not experienced in the matter.But ... just for the mental exercise, let's assume for a second that the foundation issue could NOT be fixed, like you stated in the original post.

If he is truly deranged or mentally unstable (possible with neat/bacteria-free issues)....you may be able to send a contractor (or multiple contractors) over to the crawlspace and leave some unpleasant smells, take pictures, and look for indications of illegal drugs.