To me it sounds like I should get rid of it.

It doesn't sound like she mentioned plans to move him in.Also divorce and marriage certificates are public records, it shouldn't be hard to verify her marital status.

Having access to the financials, documentation, and physical inspection will help you make a sound business decision as to proceed, or move on.

Usually rentbacks call for higher rents than market, not lower. of course, those situations I've seen have always been short term. you make it sound like this can be several months. in that situation, I would tell them they have to pay market rent, and provide security deposit.

Your goal of quitting your job and traveling sounds wonderful - and the nanny part sounds divine - I think you've found your tribe here ;)Sounds like you've already put yourself in a great position with these first two properties.

Most of the time sound goes off.

Does that sound about right? 

Now as to what you should do with your property: If the numbers make sense which it sounds like they do (are you accounting for CapEx, Vacancy%, Property Mgmt, and Repairs?)

But It sounds like all of the activity of that property has been reported on your tax return the entire time. 

Your state law should outline a process for how to take the property back if its truly abandoned, but this sounds more like it will have to become an eviction.