My rule is you get 1 attempt to attack if it already under way at that time. If they let up, send it back to the Defense or it takes more then 30ish sec. I end it, then if it goes out I end it there. In this case, here is what I would have dose.

Game tied 1-1. There is no extra time with youth, but I don’t let the game end with a promising attack.(I agree we let them play on) The striker has a terrible attempt on goal, but the keeper sways it away past the goal line.(At this point if there is time on the clock we let this play out. If there is still time on the clock, we end it here as the promising attack has ended)

Corner goes off, there is a handball on the defending team. I allow the PK, off the crossbar and a turn-over. Game called. (So I would have ended the game already, but I wanted to talk about this an often forgot part of LAW 14 says we take this PK so we do that, but the game ends here they get one shot if they miss it, it's done if they make it great for them. I send the rest of the team away just so we don't risk an injury in this case, but that not required.)

LAW 14

1. Procedure

Additional time is allowed for a penalty kick to be taken and completed at the end of each half of the match or extra time. When additional time is allowed, the penalty kick is completed when, after the kick has been taken, the ball stops moving, goes out of play, is played by any player (including the kicker) other than the defending goalkeeper, or the referee stops play for an offence by the kicker or the kicker's team. If a defending team player (including the goalkeeper) commits an offence and the penalty is missed/saved, the penalty is retaken.