FW,
Yes there are disabilities not allowed. First and fore most, the individual must be able to handle a firearm safely even with assistance i.e. know what cease fire means, know what a secured firearm involves, &c.. A very close second issue is they must be legally allowed to use and possess firearms under their states laws. We could split hairs with domicile v. residence, and travelling interstate, but you get the idea and intent.
Proof of status criteria can be found in the Adaptive Appleseed Admissions Manual. For some disabilities there are prerequisites for admission. The original team, myself and another departed AS member cussed and discussed every phrase in excruciatingly painful detail to maximize everyone's safety while not disqualifying everyone at the start.
The "spouses of deployed troops" is Official to the best of my knowledge, or at least until last Feb. when I had to step back due to a vehicle accident. I'm still catching up on a lot of the changes, and have not heard differently from anyone.
The Proof of status would be an active Military Dependant's ID Card, along with a copy of Deployment Orders or branch of service equal. Most the SBs, IITs, &c. are current or recently separated service mm embers, so final authentication would be their area of expertise.
I hope this helps a bit. Mt apologies for referring to the manuals, but there is a broad number of issues and prerequisites discussed.
Tom