I am sorry to hear about these difficulties you are dealing with. I can imagine how this might affect you and make your working life difficult. From your description, I understand that your manager quite enjoys the sense of power and authority she has and takes possibly pleasure from using this power. At the same time, she appears to lack other necessary management skills and the combination of all this creates chaos, frustration and tears to her staff. Obviously this treatment can severely affect your sense of achievement and your confidence and self esteem. In most cases, teams split (in favor of one or the other) and although this may seem inevitable, doesn't really help. People with the traits you described usually feel more settled when they feel that everyone beneath them feels intimidated and respect them completely. As you described, when you apologized things improved for a while and this happened because you "admitted" your mistakes and you stopped challenging her. But how long can you feel that you can actually do this for and why would you want to put yourself into this very difficult situation?
The situation you describe definitely needs some intervention and you sound quite alone in your role. First of all, I would suggest that you accessed some professional support so you have some supervision. If she is supposed to offer this to you, then you can always do this in confidence and pay to have someone privately. In some cases it is also wise to go above her, e.g. the director of the hospital and raise the issues that have come to your attention avoiding as much as possible personal remarks about her. You would need to show that because of the frequent problems in the wards, your staff is affected and this affects their roles and effectiveness. You would need to be very diplomatic about it, possibly raising the issue that you would like some help from above on how to improve team work and effectiveness. If you do not receive this support you could still go to HR and complain. At this point, other people would just quit and find a new job. How far you are willing to take this is up to you and how much you feel that you can take. Hopefully there is going to be someone above that can have a more objective idea of how to move forward. You should definitely be supported in this and request this from your superiors. I would advise you to think about your priorities and act accordingly. Either way, you are dealing with a very stressful situation and you need to expect some disturbance in your life if this has not already happened.
I hope this helps
Please feel free to share any feedback on these thoughts
All the best