If you buy a second Switch, you're no longer sharing the same island. There is no cloud save transfer available for the game. There will be a data recovery service available later, but it doesn't sound like it can be used to keep an island in sync between two Switches.

Each Switch will have its own island. You can use local or online multiplayer to visit the other player's island or have them visit yours to play together on separate screens.

https://www.ign.com/wikis/animal-crossing-new-horizons/How_to_Play_Multiplayer#Local_Wireless_and_Online_Multiplayer

In New Horizons, the only way to swap villagers between islands works as follows.

Let's use Julian as an example, who lives on the island of Alfa. In order for Julian to move to Beta, the following must happen, in order.

Day 1

1. The Alfa player encounters Julian with thought bubbles above his head. When talked to, he admits that he's thinking about moving out. Alfa's player can encourage him to stay, or to follow his dreams and move out.

Day 2

2. If convinced to move out, Julian will be in "packing" mode the next day. (All furniture converted to cardboard boxes). This is colloquially known in the community as being "in boxes".
3. The Beta player visits Alfa via Online or Local play, talks to Julian, and suggests Julian move to Beta. (This requires an empty plot)

Day 3

4. Julian is no longer present on Alfa, and a Julian is moving in on Beta.

Conclusion

It is possible to get friends' villagers to move to your island, but only if your friend encourages them to leave first! But at the same time, it doesn't seem possible to "duplicate" villagers in this way -- they follow a strict "one-out, one-in" policy.