I agree that you have every right to be concerned, BUT she is an adult and can behave foolishly if she pleases. That doesn't mean you should just ignore her, but I'd be really cautious about getting a background check on this guy and then showing to the rest of the family. Once you ring that bell of interference in someone else's life, you can't unring it, and you may well drive her further away. If someone cornered me with background information and had already shared it with the family, I'd probably never speak to her again -- even if she turned out to be right. It's just an embarrassment you can never live down.

That said, however, your MIL does sound like she's behaving strangely. Do you all live near each other? Is there someone near who can visit her casually and try to find out what's going on? Frankly, she sounds a bit like she's trying to use someone herself if she's looking for handyman help. I wish you luck; these are very tricky situations and people can be extremely evasive about what they are doing. I have had this happen in my own family about other problems and have had to accept the fact that I'll never learn the truth about some things.