What is the correct call when a runner misses third base; touches the plate and then goes back to third and is called out trying to score?
If the runner missed third base, then they are not entitled to score and are not in a safe position until and unless they return to third. (Sounds like this was happening).
If the runner is tagged with the ball before returning to third base, it's an out.
Touching or not touching home plate doesn't matter much here. The runner shouldn't be automatically out for doing so. Although as a little league game, there may be some additional rules that differ from mlb.