[Jim Porter]

The correct ruling on ambidexterity is that both the batter and the pitcher may switch one time per at-bat. If the pitcher switches throwing arm and the batter switches batter boxes they must stay that way for the duration of the at-bat. If a pinch hitter enters during an at-bat, then it starts all over again -- each may again switch once.

As far as bringing a glove out, I'd tell the coach he'd be surprised how far you can toss a glove without breaking it.