The couch multiplayer is tight, but there's a single village/island. You can't ever have more than one island on the console. Whomever plays first, that profile is the island representative and you have to count on that person to place bridges and do some of the more expansive questing in the game. You can have multiple other profiles sharing the same island.
In the case of the tranny being triggered by their old save data, they could make a new profile on their switch and continue to live on the island, but the animal residents when spoken to will occasionally reference people they've seen and interacted with. The nintendo animals will literally deadname the original profile that played, even if they delete that profile. They would have to delete the entire island and start over from scratch/day one, losing not only their house size and crafting recipe/catalog/achievement progress, but also their museum bug/fish/art collections and the animals they liked/had as residents, and the hassle of seasonal event items needing to be reacquired.