Mom,
Welcome to the board
I admire your courage, calm and persistence. We don't get a lot of civilians here. When we do, they're inevitably here to whine about how some official cost their team a game, elicit proof that some official cost them the game, or win a bet made during some lunch-time pickup game. Such people are usually run out of Dodge.
But as a parent of young kids, one of whom, my oldest, began playing basketball in 4th grade last year, I'd be a little upset too if my daughter came off the floor bleeding and bruised. It doesn't take a rules expert to tell when a game is getting out of hand.
Just some random thoughts for you.
First, I doubt the officiating was deliberately lopsided. It is entirely possible that the official was poorly trained and in over his head. You might think that it would be easier to do a good job on a little kids game than on say a high school game. But the truth is that 4th grade basketball is really, really hard to get right. There are sooooo many violations, so little skill, so little predicability and so many bizarre things that happen all the time. It's almost cruel that we make officials start at that level and earn their way up to easier to call games.
Second, somebody hired the ref, and you might be able to talk to that person. Take rainmaker's advice on that. The best possible outcome from talking to the assigner is that the official would receive the necessary training. As has been stated, it's hard to get good officials to work at that level. The pay stinks, the level of play is terrible and many of the parents are overbearing pains in the ***. Any official at that level who is any good will soon move on to where the pay is better, the play is better, and ... well, the parents stay about the same
The reality is the official is probably going to be some high school kid working for minimum wage.
Third, if you get no joy with the assigner, look around for another league to put your daughter in. If enough parents do this, the league is going to have to do something to stem the tide.
Fourth, if you want something done right, sometimes you have to do it yourself. If good officiating at that level is important to you, and you can't find it anywhere, then pick up the gauntlet and don the stripes. A lot of good officials got their start because they looked at some hapless fool in stripes and thought "I could do better," and then did.
Fifth, the point has been beaten to death, but this is fourth grade basketball. In my daughter's league there was no clock, no score kept and no officials. The two coaches called what needed calling from the sideline to keep the game moving along. That fact that people really care who wins or loses a fourth grade basketball game is patently absurd. The only two questions I ever asked my daughter after the game were: "Did you have fun?" and "What did you learn this week?" What else matters?