As a manager myself, you have to be very careful to not show favoritism, and even then people will still say you have your favorites. I'm not saying you are wrong, though, because clearly this manager has some definite areas she needs to improve. It's not important to show how smart you are as a leader; it's not about you, it's about your team, and making sure they have the tools and support to do the best job they can do. Sounds like she is missing that.
One thing that is missing from your post is whether you have had a discussion with her about how she is making you feel. I would recommend scheduling an appointment to meet with her and tell her what you have observed. Go in prepared, write down some specific points of things that she has said and done, and how it affected you. It will be difficult, but sometimes you have to have those difficult conversations. It may bring you both a new understanding of each other and change the relationship entirely. Or it could confirm that she is a jerk, and you can make your choice whether to stay or go.
Again, from my experience as a manager, I can't fix something if I don't know there is a problem. I appreciate it when my staff come to me, even if it's about an issue with me personally. I had one come to me a while back angry with me and she let me have it. Apparently she and I had discussed switching her to an early shift and I told her I'd look into it. I had a lot of things going on at one time, and it completely slipped my mind. Well, a person came to our unit from another area of the company and was working the early shift, so I let her continue. When the angry staff member informed me, I was without excuse. I just told her I was sorry and I had simply forgotten, that I had no other excuse than that. She looked at me and said she'd never had a manager be that honest before, and all her ideas about me playing favorites were dissolved. I was able to work it out and get her on the early shift as well.
I'm now managing a different area and this same individual recently came to me complaining about her current manager. I recommended she sit down and talk with her, and she took my advice. It has made a big difference in her relationship with that manager.
So I urge you to talk one on one with your manager and get everything out in the open.