Is it normal that upper management thinks our toxic boss is great?

Sorry for this novel. This is a big deal to everyone in our office.
Our boss is our personal nightmare. On her first day, she came stomping into our office barking orders & then proceeded to micromanage people. She plays "fave of the wk". You don't know if she is going to be nice or not. You can say hello to her & she'll sometimes replly but most days she won't look at you. Her hearing is fine.
She likes the 1 person we all despise..a lazy alcoholic who hates her job, complains endlessly, is rude to others, insubordinate to her supervisors & lies to our boss constantly to get people in trouble.
Our boss pits one against another. She bullies really nice people relentlessly since she knows they won't complain. They're always worried about getting fired. One single mother cries every wkd. She is rude & disrespectful to our hardest worker. She has destroyed the friendly atmosphere in the office. She stopped our annual Holiday Party at Christmas time, upsetting our field staff.
She was frequently off work for 6 wks at a time, because she had a hernia. The surgeon kept putting in mesh to hold the hernia in, but she broke them by putting on more wt.. She's obese. Actually it was great when she was gone! She told her supervisor that she worked so hard that she had no time to go out & do marketiing. She came in an hr late & left an hr early &spent most of the day chatting up her fave at the time & making personal calls or talking to her financial advisor who came in mthly.
She was rude to one person with a disability. She mocked her & made fun of her limitations while saying to her things like, "if you can't participate in our walking fundraiser, would a stretcher help?"
We finally got fed up and wrote a lette to head office. Our boss' immediate supervisor came & interviewed everyone. When we said our boss did something that was horrible, this woman said that our boss denied it. She denied everything. When we insisted on something, she said to 1 person "you can stop talking now". In other words "shut up". In the end, we were told that we had a problem with change. All 8 of us were wrong & our boss came out looking like a princess. By the way, on the days our boss was being assessed by her immediate supervisor, they would go out together for lunch. Upper management believes her & thinks she is wonderful & that we are all lying. It's not that easy to find a new job these days. What are we to do!? Arghhhh!