So, I'm kind of confused now... If I have a physical copy of the game, would I be able to play the same island on different switches?
Judging from other games I've played, no. Example: my boyfriend and I have our own separate switch consoles. If he's started playing Pokemon Sword on his, it won't transfer his save over to my switch. If I put Pokemon Sword into my own switch it will boot the game up as if it's never been used before.
- - - Post Merge - - -
Yes. But the way to do it when you can't use the cloud is by transferring save data from one console to another using the "Transfer You Save Data" option. This finds the other switch nearby and sends your save data and crucially, deletes it from the console you're transferring it from. So it's a bit of a pain and it can be a bit nerve-wracking once you're transferring a 100+ hour save file.
Well unless you do that but yikes I'd rather just have 2 towns o.o the sheer risk of something messing up would make me puke.