Batter picks up live ball

[falsecut]

I received this from a fellow umpire. I'm assuming that the batter picked up the ball after the runner had already crossed home plate. My dilemma with determining the correct call is that the interference rules cover plays where the batter interferes with a play at home (which in this sitch the play at home is over since the runner has legally crossed home plate before it occurs). This is youth in-house park district ball, FED rules. My thought is run scores, batter out, runner stays at third.

This is exactly how it was sent to me.
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How would you have called this?
No outs, runnners on 2nd and third.

Passed ball Runner on third scores. Man on second moves to third. The
throw from the cather to the pitcher on the play at home gets away and
the batter pickes up the ball. I was the field ump. I saw it called
dead ball. We then called the batter out. Was this correct and what
rule cover this.