What's the call on this play?

[HotCorner13]

THis play happened in an 11u game I was watching after my son's game last night:

Last inning, bases loaded, two outs, home team is batting and down by 3 runs. The pitcher
walks the batter, forcing home a run. The runner at 2nd, seeing that
nobody is paying attention, heads for home, too. The catcher tags him
high, and umpire safe. But...he changes his mind saying the first runner never
touched home plate, so the first runner was out, the run didn't count, and
the game is over.

What rule(s) applies here? The rule book states that a runner that is
entitled to a base uncontested may be put out by touching the base or
tagging the runner if he forfeits the base by going past it. I know that
if a runner returns to the dugout without touching home he can be put out
by stepping on the plate. But what if the catcher makes a play on the next
runner? Does he then forfeit his right to put out the first runner? Can
they then make a play on the first runner after the second one has already
scored? Or could the second runner be called out because, by crossing home
plate before the runner ahead of him actually did, he passed another runner
ahead of him?