"4th Out" Appeal Procedure

[nafxos]

I'm a first-year ump and had this situation come up the other night. I was the only ump working a 12-year-old summer ball game on a 60-foot diamond. 1 out, runners on second and third. Batter flies out to LF for the 2nd out. R3 tags up (properly) and scores. On the throw home, R2 tries to advance to third and is tagged out, ending the inning. R3 clearly scored before R2 was tagged out, so there is no doubt that the run will count, but the defensive team then decides to appeal that R3 left too early (which would be the so-called "4th out" of the inning, and would take the run off the board).

My question is what is the proper appeal procedure in this situation? The defensive coach asked me if the ball was still in play. My initial reaction was "no", because the inning was over. But I'm not sure that's technically correct. I knew I was going to rule R3 safe anyway, so I allowed them to go through the motions of having the pitcher take the rubber (with no batter, because there were already 3 outs), step off, and through to 3rd for the appeal. But I'm wondering how it's supposed to work, in case it ever comes up again (and especially in a case where R3 really did leave early). Is the ball still "in play" after the 3rd out? Could any defensive player simply have called for the ball and stepped on 3rd to appeal? At what point would they lose their right to appeal - once the entire team has left the field?

I remember this being discussed briefly in my certification class, but not in this detail. Has anybody else seen this in "real life"?