Sorry to hear about your relatives.

If you consider that comparison as a replacement cost, then your relative should purchase now since its under market. 

You received a gift of equity from your relative. 

To serve your relative the best, find the best listing agent in that area of Mexico, and refer the listing out to him and take a 25% referral fee.

, I can offer a technical way of doing what you want...Deed the house to the relative; create a promissory note for (trivial amount) so that you can take "deed in lieu" when you want to sell - that solves the "so I can have right to sell".For renting, just create a (master) lease with your relative where you rent it for $1 per month and have the exclusive right to sub-let - that solves the "so I can rent it out".As far as "other legal decisions" - you'd have to be more specific but with the word "legal" in there, I refer back to consulting an attorney there.

IF they want a signed letter stating that AND your relatives expect repayment, you just gotta decide whether your comfortable lying to your mortgage company.

Your relative would be selling as an individual and then purchasing a membership interest (partnership interest) in the new LLC. 

You are simply loaning your relatives money, with it secured by a STR. 

They ultimately decide when to sell or refinance, and as a passive investor in this type of opportunity you are often an equity partner who is paid your relative portion of the profits from cash flow during the hold period and appreciation when the property is refinanced or sold. 

Are use my own money but what I do is just take a screenshot of my bank account and send that in a text message to the listing agent along with a photo of my drivers license and the offer so far so good and has worked very well you could just take a screenshot of your relatives bank account they don’t need to know who his bank account it is