Situation 1: An incorrect batter (batting out of order) is at bat with a 1-2 count, two outs.  R1 is at 3b and R2 is at 1b. The pitch is in the dirt and the batter does not swing. The ball gets away from the catcher and R1 scores while R2 takes 2b on the wild pitch. The defensive coach now comes out to appeal the incorrect batter.

Situation 2: The same; but on the pitch in the dirt the batter swings for strike three and the ball gets away from the catcher. R1 again scores, R2 takes 2b and the batter/runner reaches 1b safely. The defensive coach comes out after time has been called and appeals the incorrect batter batting out of order.

Ruling in Situation 1: It is batting out of order and when the coach comes out and appeals, the umpire will bring the correct batter to the plate to assume the count the incorrect batter had since the at bat was not completed by the incorrect batter. Any advancement or outs by runners while the incorrect batter was at bat would stand.

Ruling in Situation 2: It is batting out of order but in this case it is a little different. The incorrect batter (“runner” in NCAA now) has reached 1b safely and completed the turn at bat. The umpire will now declare the correct batter out, remove the incorrect batter from 1b and return all other runners to the base they were on at the time of the pitch.

There is some confusion on this play and what happens to the correct batter and the incorrect batter when the incorrect batter is properly appealed while at bat. It becomes further confused when outs have been recorded or runners have advanced during the incorrect batters time at bat. You just need to remember, when an incorrect batter is discovered while at bat, the correct batter replaces and assumes the correct count. All advance of runners and any outs made while the incorrect batter is at bat will stand. 

If the incorrect batter completes the at bat and the defensive manager appeals before the next legal or illegal pitch, then the correct batter is declared out, the incorrect batter/runner is removed from the base, all outs on the play stand and any runners that have advanced are returned to the bases they were on at the time of the pitch.

NFHS, ASA and NCAA rules all agree. However, the NFHS rule is not well written. The ASA and the NCAA rules are much clearer

Rules: ASA Rule 7 Section 2 D.   NFHS Rule 7 Section 1 Article 2   NCAA Rule 11.11.3

NCAA rule details all the ways the batter runner can advance to 1b. Batted ball, catcher’s obstruction, error, hit batter, walk, dropped 3d strike or base hit. ASA and NFHS say “completed turn at bat with batter reaching 1b”.