Dropped Third Strike With Runner Stealing
One out with runners on 3rd base (R3) and 1st base (R1), and the batter (B1) has an 0-2 count. R1 has a huge lead at 1st base and is stealing on the pitcher's first motion to the plate. The batter swings and misses, but the pitch is juggled and then dropped by the catcher. The batter runs to first on this dropped 3rd strike but the catcher holds the ball because there is a runner on 3rd base and he does not want to throw to 1st base.
At the end of playing action, the defensive coach argues that the batter is out on strikes and, since 1st base was occupied, B1 is out and not entitled to 1st base.
The offensive coach argues that the batter should be safe at 1st base because, at the time the catcher dropped the third strike, R1 had already reached and occupied 2nd base.
What does the umpire do?
Bonus Trivia Question: What are the three rules (that were not in the very original baseball rules, but are now), that were instituted so that the defense would not have an unfair advantage to turn a double/triple play?