OP you are underplaying and it’s obvious.
You are her mother and are biased to do so and it comes across in your posts.
The weight of your daughter and other girl are irrelevant.
This it happened out of school and on the weekend is irrelevant.
What other kids are getting detentions for has nothing to do with your daughter.
Getting positive points has nothing to do with equally doing things that incur negative points.
You are missing the point from schools where kids are instructed when pushed to walk away. Not to escalate and not to carry on toward them for 15 seconds.
You said yourself that your daughter got the better of the other girl so it doesn’t matter who started it. Your daughter acted disproportionately.
You have also concluded that people have been pressured with no evidence to support other than it suits your narrative.
You believe your daughter without questioning what lead to everyone else involved having a completely different conclusion.
Your attitude to minimise what your daughter did and negate the situation suggests we absolutely do not have the full story here.
The simplest conclusion is often right and it sounds like the school had enough, took it seriously and excluded your daughter.