Welcome to the world of little league. I've seen a lot. It's hard to hold back when you are a reasonable mom. But... please keep in mind and hold back judgement. Some parents are trying to integrate children who may be ADHD, ADD, an autistic child or those who have some kind of emotional immaturity on the team. Some kids just don't handle pressure well. I have seen this for a few years. Some years, you are going to have a great team, other years it will be challenging. The saddest thing for me is, not how the children respond, but how the parents react. Yes, I've seen many 11 and 12 year old boys cry! I've also seen parents swear, kick fences and scream at their own children, with an audience - it's easy to say, which is sadder! I think it's great that they make us sign a "letter of conduct" as parents, and coaches. If your team is not doing that, I would suggest it. By not following ethical conduct, you can get suspended for 2 games.
Be patient and be that supportive mom. Approaching a parent and "suggesting to them" how to discipline their child could be a really bad move! Also be the mom who listens. You will pick up on that child who is challenged in those areas. It may be frustrating to watch that child go from temper tantrum to the field - just be sensitive. And, YOUR child may question why they act like that. 6 years old is still young for little league and, although, they may seem somewhat predictable, that age can still cry, scream and throw tantrums. I agree that a mom should "let it go" and not force a child to go out on the field, kicking and screaming. It makes a bad statement to the others.
No, you are not being petty. I, too, expect my children to finish out a season (of anything) they may have chosen, whether it's a sport or scouting, once they make the decision to join. They can quit, when the season is done. My son is on a team this year that is absolutely incredible - I'm talking about the attitude of the boys and parents!!!! Last year, it was sad. Yes, a team sport can be dramatic. What I witnessed last year has humbled my attitude to any sport that my children will ever play, in the future, and reinforces the attitude that I must be a good role model for my children. That's how it should be.
Good luck to you.