Ball becomes live when pitcher is on mound, catcher and batter is in position. Umpire SHOULD put ball back in play deeming it live. Have pitcher legally step off rubber and appeal to the umpire who is responsible for making the call. "Mr. Umpire Sir, I would like to appeal that the runner on 3rd didn't retouch 1st after the catch". Then throw it to F3 or F5, or walk it over and touch the bag (at 1st) or the runner himself (F5)
In LL I don't believe there are dead ball appeals.
In your case, a protest may not have helped, as someone mentioned earlier I think. If you protested, the umpire would have returned the runner BACK to 3rd, by rule. You would have THEN had to properly appeal as mentioned above. Which you probably wouldn't have done correctly, but then again, it seems the umpire wouldn't have known either
You probably thought, hey, he's at 1st now and not 3rd. We'll take that
The offensive coach probably thought, hey, we still have a runner, we'll take that