Am I being set up to get fired?

I had a similar situation at my job. Three women all in management. One of them was harassing me, none of the management did anything to help me and wanted nothing to do with it. The other two, my manage and supervisor were practically besties with her and not only sided with her but protected her. It wasn't until my supervisor and another female coworker were being harassed by the same woman that management and corporate actually started investigating and eventually leading to her firing. Til this day I still have not receive a single apology to anyone, in fact I actually received a write up during the investigation. My supervisor plays it off as if we're friends but still reports me for the dumbest things. And my manager pawns off her work and other peoples work on me.

All I can say is this. Grit your teeth and dig in your heels for as long as you have to and find another job. That's what I'm going to do. Not even going to give my two weeks notice. I'm sorry but I absolutely hate women in management. Most of my bad bosses were women. Not the first time I had female coworkers and bosses conspire against me. Actually lost my job to that once.

document everything...only advice i can give you

I recently went through something like this but I was part business owner. I basically got massacred by people I thought were friends, and it was pack mentality as they took me down. I got asked to step away from the business for the sake of the business, but despite hitting rock bottom and still trying to pick myself up after all this, I am trying to see it as a blessing in disguise. It was a toxic environment where everyone was two faced and back stabbed. As a part owner I couldn't just leave as I have a financial interest in the business, but I am now looking at other options for work. My advice would be to find another job, preserve your mental health, and walk away with your dignity, because you may document and fight them and take it further etc, but you need to be prepared for the possibility that it may be a tough road ahead and may be hard to fight. When bullies collaborate and gang up they can be ruthless. Just remember though that Karma doesn't forget an address, and these kind of people get what they have coming. Take care of yourself and let the universe take care of them. Think about it. Do you really want to continue to work in such an environment and if you win a case against them is it worth your time? Wish you all the luck in the world, and keep the faith that you will be okay, because good people also get rewarded.

I can feel you, understand your frustration and disturbance.
Typical favouritism, gossiping and selective preference scenario.
You will have to decide - would you like to wallow in the mud with them, gossiping, spying and scheming behind other people's back? Or would you prefer to rely on hard work, integrity and accept being not-so-popular with them, not a member of the inner circle?
Let your heart and mind tell you.

Yes you are being set up, problem is evidence of this is very difficult to come by it'll most likely be your word against hers, I assume there isn't another level you can go to but if there is the sooner you can talk to them the better -as long as that person isn't in the clique too. (When you read or hear stories about people getting revenge for these things they are generally fiction.) Do your best to collect anything that may help but don't be upset if it doesn't work out.

You should do your homework before you take on a job.

If she's dating the HR manager there's basically nepotism going on. Nothing you can do about that. Even with evidence. The nepotism is cross departmental. You're talking your word against three others. Two in higher positions than you and again cross departmental.

They would have to remove three to your one person's. No company would do that.

As long as you take steps to cover yoursel, ie; times, dates, what was said the you will have a case against them if you are removed for no apparent reason.
Those sort of people get where they are, not through skill but kissing backsides and licking boots.
What they deserve is a forceful clip around the ears.
Keep your spirits up and try not to let them get you down.

Record any evidence you can (within the law) it sounds like you work for a small business? So no HR?

Yep there's a lot of warning signs there. Any boss that does sneaky promotions has already stabbed you in the back