You don’t need Internet to use wifi. A router in her home can connect to the controller. An outsider can’t connect to the controller from the internet, because it won’t be connected TO the Internet. Think of it as an intranet.
A 2.4 gHz wifi signal can go miles with the right transmit and receive antennas. I’m sure 5gHz can to. Actually, search for “pringles cantenna”. Can also use old DirecTV sat dishes for point to point (using the pringles can as inspiration).
I’m guessing your sisters device doesn’t have the antenna in the perfect orientation and the router antenna needs to also be oriented perfectly to get the longest distances. We use to have lots of apps that helped done tune devices back in the days of PDA’s & wardriving w NetStumbler.