You bring up a good point. I don't actually own the house myself so I can't ultimately make any final decisions on selling it or where those profits would go. If it were sold I think the money would go to my G-ma and then eventually to the kids and grand kids. Personally for me I don't want her to sell it as it was a place my G-pa really wanted to leave to his daughters and grand kids, plus the view is just amazing. I also think as it's an island residence the value is only going to go up in the next 10 to 20 years as those kinds of properties become more scarce (this is nothing more than my gut feeling). If it didn't have sentimental value I would look for other options.
In that case, shouldn't it be your grandmother's decision? Or, if you want to keep it, you would be paying all the expenses?
I realize I don't know your relationship with your grandmother, but it seems a bit unfair to ask her to keep this property that belongs to her, ask her to pay the expenses (or even half, as above), and then use it.
Taking over all expenses seems the right thing to do. And then, hopefully, getting it rented to cover those expenses and then some seems the Mustachian thing to do. And of course giving her the extra profits (which she may even let you have, since you're doing the work of dealing with a property manager, etc.)
Just a moral issue to consider, money aside.
In any case, I think you're right about the property manager being the only way to go.
Do you have any other friends in the area? Maybe they could manage it, at the cost of letting them stay there free some weekends...