You do have my sympathy. At one time or another, most people have to deal with a poor work environment. At one time or another, most people go through a period of feeling unappreciated and unfairly treated. That doesn’t make it okay. I just want you to know that your situation isn’t as unusual as perhaps you think.
In your case, management is on that woman’s side, not yours. Chances are that things won’t change unless she does something that management finds upsetting.
Normally, I’d tell you to start looking for another job, but you made it clear that isn’t an option for you at this time. Therefore, I hope you can find a way to take this less personally and to separate your identity from that is going on at work. You are not your job. You are an intelligent, thoughtful person whose letter shows maturity and fairness. Furthermore, you have a history of being a successful tutor, which says to me that you are patient and skilled as a teacher. No one can take those attributes and skills away from you.
Even though you need to keep your present job, perhaps you can consider taking on some tutoring work privately or you can look for a part-time position with another company. Either one would help you financially and would give you another source of recommendations for when you move.
I wish you well,