I think the problem with refinancing the home is she wouldn't be able to qualify?
You really need to do the math both ways (keeping the house versus selling) and figure out what you can manage.
IF you can refinance the house to pay off ex OR if he will stay on the mortgage while you make payments to him towards that $100k while quit-claiming the deed to you - you have to figure out if you can carry that financial load.
Alternatively, you could sell the home, take your $100k split, buy a condo if mortgage and carrying costs are less than rent, OR, if that's going to be more expensive than renting, you could rent.
OR you could take your $100k to some part of the country where that buys you more in terms of property. How wedded are you to staying in the islands?
It would be nice if you could afford to keep the rental property and be in a position for the rental to pay your mortgage at some point when you retire but that seems like a big stretch given your current financial status. You're in the somewhat difficult position of having to plan for your future retirement while still raising a small child.
(And speaking of retirement - how does your new citizenship affect retirement? Are you allowed to double dip, from Social Security here and whatever you had in your home country? Is one better than the other? Could you end up with just half the retirement benefits you should have because you only get credit for half a career in one country? Were you married for at least ten years? You need to factor this in to the equation. Is it worth it to stay here if it means less money to retire on? )
