While mental disabilities are recognized as handicaps and are covered under ADA/HUD/Etc, for the sake of parking, I have yet to see a state parking form for a handicap parking permit allow mental health issues. All the issues revolve around being ambulatory.

A doctors note stating "My patient has x condition, so it is my belief they get to supersede laws or regulations" is an opinion, not a fact which allows this. Basically, its an acknowledgement by an expert that is vouching for the person they aren't making the condition up. But that doesn't mean you have to follow the recommendations.

They family is not requesting a handicapped space, say because a child is wheel chaired bound. The children are of driving age, and ambulatory. How can these kids drive, but get so anxious getting to their vehicle they have to park close to the home? Not to mention parking anywhere else. Driving is way more anxiety inducing and stressful than walking to your car in a normal neighborhood.