Nickname, do you know what the motivation might be, behind the SM's actions. I am sorry you are going through this, it sounds awful, but do you know why she is taking such an excessive approach? Have you ever been able to talk with her, or has the situation been so fraught that the opportunity for dialogue just doesnt exist?
Just so you know where I am coming from (and its a very different circumstance from what you describe) I have been hated by my DSSs mum from literally day 1 As far as she has been concerned, her mindset has always been that I am "a nobody", just there to steal her child away from her. Several years ago, I arranged to meet her and she may as well have spat in my face, she just never gave me a chance. Yes, I have always wanted to have a loving relationship with my DSS, not steal him away. Instead, I was told I shouldnt have anything to do with him, nor even try to get close to him " he isnt your's". How unrealistic when I was in the relationship with my DP and needed to ensure DSS - as an only child - did not feel left out in the cold. DP secured 50/50 shared residency, EOW (this was the year before he came into my life) which has panned out really well for DSS, he has a strong bond with both parents, and after some fraught times, everything has settled down.
It is a very difficult line to cross for SPs, some people are happy - or have been forced- to remain "one step removed and others have the opportunity to be involved, and in doing so it can seriously over step the mark (and depending on circumstances, it is interpreted that way - each situation is unique). Sometimes a SM feels unable to get involved and the mum is critical they don't care!
When emotions run high, people do ill-considered things and perhaps even over-react/over-compensate. Maybe she is doing that. I am hesitant to think of her as wicked and evil, I think there could be explanations (does she have her own DCs? Could DD be the daughter she never had?). She sounds like she is controlling things excessively and needs to pull back.
I promise I am not trying to excuse or minimise the behaviour re hair cutting etc but trying to understand. Maybe your bottom line is that you dont want or need to understand (which I fully appreciate given the circumstances you describe) and you just can't stand the woman! I dont blame you, she is seriously tredding on your toes. I am sure my DSSs mum thinks I am "not needed on voyage", just being in his life, full-stop, but I wouldn't feel right being the remote, non-involved "blob" that she would rather I were.
Fwiw, re haircuts, DP has always taken DS for haircuts whenever required, no permission sought. He needs to have rather short tidy hair for his cadets activities, so one might argue he ought to text DM each time....in recent years I have taken him to the same place if DP cant do it and it would quite frankly be "red rag to a bull" if I sent her a text (full stop! definitely a no-fly-zone). A complete change in hairstyle, especially for a girl, is a very different kettle of fish, so you have every right to feel upset and shocked at the lack of respect shown to you.
These are just a few thoughts and perspectives, nothing more than that - china's advice is brilliant!