She has never mentioned to me that the moisture came to her daughters room.

Is the moisture resistant drywall in the bathroom and kitchen worth it?

You want tile or vinyl in the wet areas, such as kitchen and bathrooms to prevent buckling from the increase in moisture. 

Have you encountered any moisture issues so far? 

For construction costs I’d factor 200,000 250,000.Things you need to check: Service size of water (might need think of a pressure booster), electrical service panel, spray foam entire home I would recommend closed cell spray foam, since this is higher r value and moisture barrier. how is the structure of the building?

Yet ants are not hard to rid of as they usually arrive due to moisture / food.

I sent my plumber in before we closed to stem the damage.On top of that the subfloor in the bathroom, and hallway just outside it, on the main level will need to be replaced as a consequence of pets urinating in that location for years - when we bought the property, the moisture readings in that area were off the charts, it was only later we figured out why.

He says there has been un-handled moisture damage in the bathroom and the kitchen countertop needs to replaced, I know it true ( showed up in the property inspection) . 

So I'm thinking quarterly would be viewed as generally acceptable in my area, even though it is not a common practice in my experience.I'm probably going to phrase the inspections as geared towards identifying any potential leaks (pipes, windows), moisture issues, etc, to protect the tenant's home, and ensure it stays safe and healthy for them and their family.

I’ve had people come inspect the crawlspace for leaks, spray for mold, and installed increased ventilation in the bathrooms to cut down on moisture.