I guess my family is just different. When we visit more than an overnight or two, we always stay in a hotel so the hotel thing doesn't seem weird to me (the 10 year old alone does! But OP staying with him does not). Who pays, varies. When we go see my parents, they usually pay for the hotel. But I'm sure they'd much rather we stay in the hotel than their house (as would we) and we don't consider it cruelty. If we stay just one night before a big trip together, we will just crash there, but if we're staying for a week, it's not in someone's home!

We wouldn't put a kid in their alone, but when my husband's kid brother came (around the same age -- he was either 10 or 11, as his birthday was right around the visit), we stayed in a hotel for part of it, to be closer to the attractions and have a more fun place to stay. There were a few nights they stayed there I didn't even, but that was due to it being a 70 minute drive from my work (and me not being off work the whole time; my husband was!), not due to me not wanting the kid in the house.

We've not had any family kids for longer than 2 days other than that. But even adult visitors rarely stay in our guest room for long.