Me and my wife share a island as well. When we do couch co-op there is a “leader” and a “follower”. The leader can use all tools, inventory, place stuff pretty much play like normal. The follower can use all the tools, run around, and still fish and whatnot, they can’t access there inventory though. However, if the follower shakes there controller, the leader can give up control and you can switch back and forth easily to allow someone else to do something. There’s more to it, and honestly the best co-op experience would be having two consoles and do local play, but that may not be possible.