The way we played Red Rover when I was in gradeschool (not so very long ago 🙂 was the two teams would be on each side, hands linked.

Then someone from one team would shout “Red rover, red rover let ____(name of kid) come over!”
Then the kid they named had to run over and try to break the chain (no going under allowed). Usually they know where the weakest link is… If you don’t get through, you have to get in the chain. The game ends when one team has everyone. I think if you DID break through, you would get to go back to the other team? Or maybe you sit out the rest?