13U Runners on third and second, one out. Fly ball to center. Runner on 3rd tags and on the throw home the runner on 2nd fails to tag up and moves to third. After the play at the plate the ball is retrieved by the pitcher who receives instructions to go to the mound (ball was live at all times) and wait for the umpire to call for a pitch and then step off. He steps off to appeal to second and throws wildly to the shortstop who must leave the bag to make the catch. On the wild throw the runner breaks for third inducing the shortstop to throw home. He slides in safely. We go through the routine again of acquiring the pitcher's plate and stepping off and appealing at second. I disallowed the appeal since a play was made after the pitcher had acquired the rubber - analogous to the pitcher committing a balk I reasoned.
It depends on the rules. Under FED, you allow the appeal because the action of the offense initiated the intervening play at the plate.
Under OBR, you do not allow the appeal because there was an intervening play following "relaxed" action and prior to the appeal. Under OBR it makes no difference who initiated the action that resulted in the intervening play.
I wish coaches (and some umpires) would learn that if the ball remains live, you don't have to give the ball back to the pitcher, toe the pitcher's plate, step off stuff. All you have to do is make the appeal. Also, you can make the appeal by either tagging the base or tagging the runner. This all would have been avoided if the defense threw the ball to third base and F5 had tagged R2 and made the appeal that way.
Under FED, there's a dead ball verbal appeal. All the defense has to do is call time tell the umpire they're appealing. What could be easier?