Who wins the side pot in an All-in scenario?

Just played a home game, and there was some discussion about a scenario that occured there.
Here's what happened, and how we solved it.
The question is, was it correctly done?

Player 1 on the short stack went all-in after the flop.
Player 2 (me) and player 3 called, and created a side pot, which they continued to bet into during the turn and the river. No cards were shown as betting still occured until after the river.

When all bets were called, it turned out that the short stack player had the best hand. So he got his rather small winning, from the main pot.

The problem was about the side pot. We solved it by awarding the best hand among player 2 and 3 as the winner of the side pot, which was player 3 .

I argued that this was wrong, with the stand point that there can only be one winner in a poker game, and that the side pot should be canceled and the bettings returned to the players. I was overruled as stated earlier, and lost both the main bet to player 1, and the side bet to player 3.

What is the correct thing to do in this situation?
Should Player 3 in fact have won the side pot as we played it?
Or should the side pot have been split among the side pot bettors.

// Fresh meat.

Player 3 wins the side pot

pLAYER 1 wins the main pot (the small one)

Then PLayer 3 wins the side pot.

Yep, player 1 gets the main pot and player 3 gets the side pot.

Here's the reason why: For the main pot, you were betting that you had the best hand between the 3 of you. You didn't so you lost to player 1. For the side pot, you were betting that you had the best hand between just you and player 3. You didn't, so you lost that to player 3.

Good luck at the tables, and welcome to FTR!