[senior]

Chris, there are only so many choices you have to pick from during any given time. From your story, and the edited version also, I would say you did well, considering the circumstances.
Several things could have happened to improve your situation, (hindsight is always 20/20), the most obvious to me would be having a partner already assigned to this game, because of its' seeming importance. Scheduling someone to work alone in your described contest is an invitation to have trouble. Since you were fortunate to secure the help of a partner, more problems were prevented from occurring.
As already suggested in the responses, you may prevent these problems by requesting help in the form of the UIC or TD being present when this team plays, due to the reputation they have established.
There is no excuse for the boorish behavior from the parents, but that is not your problem to fix. You need to request attendance in the form of Board Members or League Officers to deal with them. They have no respect for you, or your efforts on behalf of their little darlings, but perhaps would at least consider listening to someone their own age, especially someone in a perceived "official" capacity.
Good luck in your efforts, but don't expect a miracle cure. One of the "downsides" of umpiring is the "flak" factor. Keep working to improve, ignore the negatives, and one day you'll get to where it won't bother you much. There are, believe it or not, folks who appreciate your efforts, but they will never be as obvious as the jerks who don't.