BOO question
 

Situation: first, second and third batters. Numbers are 1, 2 and 3. Batter 1 is supposed to bat but batter 2 bats and hits popup for an out. Before next pitch defensive manager appeals and says 2 batted and 1 should have. Appeal accepted and 1 is called out for not batting when they should have. Since 2 batted and and popped up for an out, does the out stand and then we put 3 up to bat or do we simply have #2 bat again and not count the pop up out as an out?

What rule book are you using?

Fed
#1 is declared out
#2's time at bat is negated
#2 returns to bat in the proper lineup position with 1 out

If no appeal is made and a pitch (legal or illegal) is thrown to the next batter (#3), #2's at bat stands and #3 becomes the legal batter

ASA

#1 is out for failing to bat in the correct order.
#2 is out on his popup.
#3 bats next, with 2 outs.

Two different twists on the question.... ASA:

SIT1: 1 is suppose to bat and 3 comes up and flies out. Defense properly appeals, so number 1 is called out for not taking his/her turn at bat and number 3's out stands. Would it then be #2's turn at bat with two outs? If #2 gets a base hit, is it then #3's turn at bat?

SIT 2: 1 is suppose to bat and 8 comes up and flies out. Defense properly appeals, so number 1 is called out for not taking his/her turn at bat and number 8's out stands. Would it then be #2's turn at bat with two outs? Who bat's after #7, two innings later?

ASA

Sit 1: #2 bats with 2 outs, followed by #3

Sit 2: #2 bats with 2 outs, and the games resumes normally

Yes

No, #3 has used their turn at bat. The next scheduled batter would be #4

Same as above, yes.

#8

If #2 gets a base hit, is it then #3's turn at bat?

No, #3 has used their turn at bat. The next scheduled batter would be #4

7-2-D-2-c

The next batter is the player whose name follows that of the player called out for failing to bat. Exception: If the incorrect batter is called out as a result of their time at bat, and is scheduled to be the proper batter, skip that player and the next person in the lineup will be the batter.

The way I read this, if #1 is supposed to bat and number #2 bats instead and makes an out, and the defense appeals the BOO, #1 is out, #2's out stands, and #3 would bat. The incorrect batter (#2) has been called out as a result of his time at bat and is scheduled to be the proper batter, since the lineup would continue after #1. In that case you skip #2 and go to #3.

But if, as in Situation 1, #1 is supposed to bat and #3 bats instead, then #1 is out, #3's out stands, and #2 would bat, followed by #3 again.

Casebook Play 7.2-9
Bases loaded, B4 scheduled to bat, but B4 comes to bat instead and ground into a double play, resulting in R3 being forced at 2B and B5 out at 1B. The defense appeal B5 batting out of order.

RULING: All outs that occurred before the appeal stand. Any runner that advanced are returned to their original base. Because of the appeal, B4 is declared out for missing their turn at bat for the third out of the inning. B6 leads off the next inning. (7.2.D.2.b)

Think about it. It isn't possible for a player to make two outs in the same inning in which a team does not "bat around". B5 had his opportunity and was called out. It is the same as if the batter due up is on base or previously scored in that inning.

Casebook Play 7.2-9
Bases loaded, B4 scheduled to bat, but B5 [my correction] comes to bat instead and grounds into a double play, resulting in R3 being forced at 2B and B5 out at 1B. The defense appeal B5 batting out of order.

RULING: All outs that occurred before the appeal stand. Any runner that advanced are returned to their original base. Because of the appeal, B4 is declared out for missing their turn at bat for the third out of the inning. B6 leads off the next inning. (7.2.D.2.b)

I have no problem with this ruling, since it is covered by the "Exception." The next batter after the batter called out for failing to bat in the correct order (B4) would be B5, but B5 was put out on the play, so he is skipped over.

But if B6 batted instead of B4 (parallel to #3 batting instead of #1 in Situation 1 above), then after the double play stands and B4 is declared out, B5 leads off the next inning, followed by B6.

In other words, you skip over B2 if he batted instead of B1 and made an out. Or you skip B5 if he batted instead of B4 or made an out, or B7 instead of B6. But if any batter other than the one immediately after the proper batter makes an out, and the defense appeals BOO, the out stands, the batter who should have batted is out, and you simply continue with the batter after the one declared out for failing to bat in the proper order.

Thus it would be entirely possible for a batter to make 2 outs in the same inning without his team batting around: B3 bats instead of B1 and flies out. Defense appeals. B1 out, B2 bats and singles. B3 flies out again. Or take the second situation above: B8 bats instead of B1 and flies out. Defense appeals BOO. B1 is out, B8's out stands, and B2, B3, B4, B5, B6, and B7 get hits. B8 then flies out to end the inning for his second out of the inning without his team batting around (B9 didn't bat).

Casebook Play 7.2-8

With no outs, R1 on 1B and B2 scheduled to bat, B4 comes to bat instead and grounds into a double play. The defense appeals B4 batting out of order.

Ruling: The double play stands and B2 is out for missing [his] turn at bat, resulting in the third out. B3 will lead off the next inning.

Note that the ruling does not add "and B4 will be skipped over."

It is the same as if the batter due up is on base or previously scored in that inning.

I can't find any mention of skipping over a batter who "previously scored" in an inning. Where does the book cover it?

New inning.

You're correct, there is nothing in the book and I made a presumption to that point. You would think that if someone reached base and scored, the defense would have caught on. You are correct though, the book only addresses runners still on base.

Yeah, I have to agree with greymule on the "previously scored point". Here's my case play:

B1 singles. With B2 due to bat, B5 bats, and homers. B3 bats and strikes out. B4 bats and singles. B5 is now the next legal batter.

Rationale: once B4 bats, that legalizes B3. The proper batter after B4 is B5, even if B5 batted out of order earlier in the inning.