re: I experienced my first baseball mom this evening at a scrimmage between 7 year olds

Lol, that is nothing. You wan't to see some action, step into the world of motocross racing. Especially at the big nationals, and the younger the kids the worse the parents are.
Every year at the biggest race, the 4-6 year old 50cc class is insane. I will literally go hang out at the tent where the officials are because it's inevitable that some parent is coming in screaming about another kid cheating and wanting to protest. They will throw up the cash and whomever beat their kid will have their bike torn down and given back to them in boxes. If it passes, they get to keep the cash.
Couple years ago, a guy walked in and protested the entire top 10 finishers. Threw down several grand to make it official. When 2 of them were found to be on cheater bikes, the drama really blew up. There were death threats and law suits, for the 4-6 year old class.
It gets rowdy, but in all fairness at this level they have exponentially more money invested than any travel ball parent.