'Rude' doesn't equal 'a horror'.
I think that there's an awful lot being assumed about what the teen did or said, because there's bugger all filler. About the initial argument anyway.
Once again, I feel OP has been quite slanted in her story, about her own input into the initial argument (very much glossed over, dd was just horrible to her, over something really quite trivial), for example.
If you leave marks on a person, you're leaving yourself open to criminal prosecution. Even if it's your 'vile brat' of a 'manipulative' daughter.
Who did she leave marks on? How many holes in the wall has she put in the family home?
Who do we think is bigger, stronger, holds the balance of power, here?
But apparently no-one can figure out how to effectively parent a 16 year old without leaving marks on them in this family. And that, of course, is the 16 year old's fault.