I have 15yo and a 10yo DDs. Some random thoughts:
Can you talk with your DD when she is calm? What does she say about how she is behaving? Are you getting any support from school such as ELSA?
10yo can be hard, hormones raging, girls all trying to be towards the top of the pecking order at school. If she is y6 there is also the angst of SATs and moving on to secondary school.
I would be tempted to remove all privileges such as phone and tablet. (Does she really need a phone anyway?). They are then provided for a fixed time each evening provided behaviour has been good. Poor behaviour (including rudeness) results in losing time from the electronics.
You could go 'extreme' and remove stuff from bedroom and she only gets back when behaves well.
I went to a parenting course where they advocated 2 punishments only for teens (I know yours isn't there yet): 15mins loss of phone, or 15mins earlier to bed.
Would also say pick your battles. It wouldn't have been the end of the world if she didn't have a shower, or maybe showered next morning.
Don't get into physical fights. You may win now but you won't in 5 years time. If she won't move from a room, then remove yourself and your attention.
Keep your DS safe, removing him from her as needed.
Stay strong. good luck.
(Oh, and given that you are concerned that your DD may be going the same way as the neighbour, I'm not sure it was necessary to mention the neighbour is adopted. It made me uncomfortable, as if you are tarring all adopted children with a 'wild' tag. My adopted 15yo is currently a delight.)