Batting out of turn

Question
Little league, continuous batting order, regular season.

Toward the end of our opponent's lineup, batter A had a 2-2 count, but we threw out a baserunner attempting to steal 2B for the third out.  The following inning, the opponent sent batter B to the plate.  We saw they were batting out of turn, but weren't sure when to ask the umpire for the ruling.  We waited for our pitcher to throw one pitch, taken for a ball.  We then called time and told the umpire we believed batter A was the proper batter, since he had not completed his at-bat when the third out was made on the base path the previous inning.  All agreed, and we asked for the out for proper batter, which the umpire gave us.  Batter B started his at-bat from scratch.

However, in reviewing baseball rules, I wonder if this was the right call by the umpire.  Did we need to wait until batter B finished his at-bat if we wanted to have batter A called out, sending batter B to a fresh at-bat?

From a ruling standpoint, what's the call?  From a strategy standpoint, how would you play it if you were the manager, considering all batters involved - including upcoming batter C -  are not likely to get on base, and you saw batter B coming up to the plate improperly?

Thanks,

Jim, Shreveport

Answer
Jim,

In your situation, Batter B would have just been replaced by Batter A, and Batter A would have assumed the count of 1-0.  However, if you would have waited until he reached base and appealed before the next pitch or play, Batter A would have been out, and Batter B would come back up to bat.

As for strategy, I would have waited and made the proper appeal for the out in that situation.

I hope this has helped.

-Martin Hoover