I really do love Alex's backstory.... I think it's one of the best in Stardew.... I have this head cannon of Dusty being from Alex's past life when he was living with his parents, being one of the only good things he had in his life while living with his father...and when his mom died, George and Evelyn didn't have the heart to leave Dusty behind because they knew how much he meant to Alex. So they brought him to the valley, but decided to keep him outside as a sort of compromise. George doesn't like dogs, but the man def has a soft spot for his grandson.
Of course this would make Dusty a very elderly dog when the farmer arrives at the town, but eh. I kind of like the idea of Alex loving his old mangy dog who's been with him forever
I want Dusty to live on the farm with you when you marry alex so bad!!!!!
(EDIT: also yes i had to give little Alex that country boy little kid mullet that some parent's give their kids. If you think that kid wasn't rocking an ugly little awkward sporty kid mullet, idk what you're on)