Susan,
Sorry to see you're having a rough time at work. I don't know of much advice to give except for this:
First and foremost, in order for you to be successful and happy, you
must have the support and professional guidance from your immediate supervisor. Your boss must not be taking sides with anyone, she should be guiding and managing her subordinates in a supportive way so they all work well together to meet the overall objectives of the department. Giving preferential treatment and picking favorite employees is disruptive to the overall department.
From what I read, your supervisor is not supporting you. By making accusations and failing to give you "specific" examples of what you are doing wrong. Instead, she is making vague statements about your bad reputation, breaking equipment, displaying anger and getting work done in a timely manner.
If you want this job to work, you need to be the driver. What I mean by this is for you to be active and proactive in making change. Obviously your boss and the bully are being reactive, so you need to be proactive. I suggest that you arrange a meeting with your supervisor. Ask for SPECIFICS of where you have a bad repuation, broken equipment, displayed anger, did not meet deadlines or complete work. Then, after you have that information, put the ball back in your supervisor's court by asking your boss to HELP you improve. Ask your boss to help you develop a personal improvement plan (also known as a PIP to HR people). Establish SPECIFIC (not vague) goals, timelines, behavioral changes, listing these goals as quantative (meaning measurable). Then, at specific intervals (weekly) meet with your boss for an hour to discuss your goals, where you are succeeding and where you still need to improve.
Be humble, take ownership and accountability for your past actions at work. Tell your boss you are turning a new leaf and you need her help in order to succeed. Don't badmouth or blame anyone else...remember that this is YOUR issue, not the bully's and not the boss's. No blaming anybody but yourself. Take this non-defensive approach to build up your foundation and go from there.
If you take this approach and
drive your own improvement plan, communicating on a regular basis with your supervisor, you will not only show you have ambition to improve, but you will also begin to establish an opportunity with your boss to have free and open communication, which can only lead to good things.
Think about it and start working on your own PIP. Ask your boss to collaborate with you on your PIP. I think things will work out. Talking, communicating builds good relationships.
Good luck and keep in touch because I would love to hear how things are going (and improving)!!

SNA in AK where spring is slow to come this year!