I work most weekends, but in exchange we take at least 6 vacations per year.

Consider Offering Incentives: If the tenants are unable to pay the full amount of rent owed, consider whether offering them a financial incentive to vacate the property voluntarily could be a viable option.

FHA - yes you can purchase 2-4  and one tenant needs to vacate for you to occupy. 

A lot of lake home options that can make for an easy Vacation home 10% down and then transition into a rental.

I'm not sure what part of FL you're in and what properties cost there but could you buy something locally and rent it out or do MTR or STR (to traveling nurses or corporate professionals and/or people vacationing)?

Also, it tends to ensure much better renters--families on vacation, not groups of eight partying for the weekend.

I’m buying a home now and will be renting the home I’ll vacate, so my old house will become my first rental property.

I am somewhat familiar with living in vacation areas in which housing prices are disconnected with local wages. 

Yeah, maybe there's no art scene and the weather is crappy - that's what vacations are for. 

The house is paid off free and clear, but we have no intention of selling it; we want to keep it in the family and turn the lot into a vacation home, Airbnb, or even a rental.