Many counties now have auditor sites that list home ownership, searchable by name, address, etc. If you think they may be home owners (as opposed to renting), you can see if the county has such.
Many counties also have clerk of court websites. While privacy issues may limit the amount of information available, you could at least do a search on her name and see if there's any record at all. Ours has any court issues, including divorce, and motor vehicle citations.
Even if she doesn't know her "condition" name, she certainly know her physician's name. Once she gives you that, check to see what type of doctor she's talking about (I mean, if it's a OB/GYN that would somewhat discount the terminial brain issue, no?).
What's the name of the kids' school? You could also then do a search for that.
The little one has a "mental" age of 3 but he has an IEP for ADHD? Um, ok.
I'm just trying to help you with that "resolve"...... you have my thoughts and prayers.