I’d pay off the rental first

Then when you sell it you pay off your house with the proceeds and bam both houses are paid off!
But if you payoff your house first, you have a paid for house, but you still have the rental to pay on while your dad lives there.
Logically, they both payoff the same, but mentally paying off the rental is like paying off a debt. When that is paid for and you sell it, you get a big fat check! Then you take that money and pay off the mortgage on your house. It feels like found or made money!
Notice the word feels, it feels different than just selling the rental and giving the money to the bank to payoff the mortgage on the rental.
Its all about the excitement of being gazelle and paying of the rental and then reaping the benefits by being able to use that money to payoff your mortgage.