Improper Batting Order

Question
Similar to a question asked previously, but....
Runner on first; batter hits to shortstop, who throws runner out at 2B for fielders
choice.
Defense appeals batter as improper, and proper batter is called out.
What happens to the runner who was called out on the fielders choice? Does he
return to 1B, or does the out stand?

Answer
The runner at second would remain out and the batter would stay at first. Also, the proper batter would be out as well making two outs on the play.

Rule 6.07(b) When an improper batter becomes a runner or is put out, and the defensive team appeals to the umpire before the first pitch to the next batter of either team, or before any play or attempted play, the umpire shall (1) declare the proper batter out; and (2) nullify any advance or score made because of a ball batted by the improper batter or because of the improper batter抯 advance to first base on a hit, an error, a base on balls, a hit batter or otherwise.

This is the rule that has the most relevance to your question. After re-reading all of the rules regarding batting out of turn, I stand by my answer.