Interesting discussion. Been watching various age groups for 6-7 years, and here's my take:
1. Truly dirty players are rare. It is a physical game and most girls playing club soccer are more aggressive than average, so you get lots of collisions that over-protective parents wail about, but don't amount to intentional dirty play. Had one kid on our team who really loved the physical part of the game. She was little, too. But she ran full speed into 50/50 balls and loved it when she knocked opponents down. Sweet kid off the field though. But she got lots of yellow cards and a PK once that cost us a game. Our coach over time taught her how to channel her aggression, but it was a process. I wouldn't say she was dirty, but plenty of opposing parents probably thought she was.
2. It is a frustrating game sometimes, and I've seen plenty of decent kids lose their tempers, get frustrated, or seek "revenge" for something said or done in the heat of battle. This results in obvious fouls and some extra forceful body checking that, while within the rules, seems unnecessary. Doesn't make it "dirty," but out of control, yes.
3. Eliminating dirty play is for the refs to handle. Just like you see in professional sports, a really good ref will see what is happening within the game and notice when a player is getting too edgy or if a couple of players are going at it a little too emotionally. They pull them aside and talk to them. They will pull the captains and talk to them. They will talk to the coaches. They will give out cards and ejections if they think it is getting out of hand. That is how it gets stopped. A ref stopped one of my kid's games once to lecture both teams about getting too feisty, and afterwards they all shook hands and smiled and it ended up being a great, clean game. Coaches aren't neutral arbiters of the game. They are in the heat of the battle, too, so it isn't realistic to leave it up to them to pull an over-aggressive player when that player might win them the 50/50 ball that turns the game. That's why the refs are there. If you get a weak or inexperienced ref, that's generally when "dirty" play evolves.
4. As for how to handle it as a parent, I just tell my kid that the ultimate revenge is to win the game so don't let the fouling or physical play distract her from focusing on her job and responsibilities on the field or her technique. That doesn't always work, but you do the best you can. I give her examples from professional sports or athletes who are able to block out the nonsense and focus on their jobs vs those who get caught up in the extraneous stuff and lose focus (see Phelps vs. Le Clos in Rio).
