My scheduler has been trying to get me fired since day one

I’ll keep the story brief, and names vague, but recently (about a month and a half ago) I started working at a commercial HVAC retailer as a service technician for a particular brand of VFDs after separating from the navy. I was originally hired to work on the three lines that they sell less of, so that they could sell more of those products, since their current tech is extremely busy being the only tech in the state qualified to work on their main line of drives. Normally they have a backlog of service calls to get through so I was told to work as a backup for the main tech for now, and once things slow down I could start learning how to work on the lines I was hired for.

A month and a half in, and things have slowed down drastically. I’ve been spending a lot of time at the office staring at 4 cubicle walls, and the scheduler (who, to clarify is essentially supervisor of the sales team, not the techs, but still has say over what I’m up to, to a certain extent) has been sending me home early often due to there not being any work, and not really any way for me to fake it and look busy. I’ve had two meeting with HR already, the first of which was an ambush meeting. I was originally told that the meeting was to discuss the expansion of one of the drive lines I was supposed to be running, so I was very confused when the meeting starts, and it’s the scheduler, HR, and my boss. My boss says he is upset that I missed a class (a class that was at 4am, that I was given the wrong address for), and says that “it’s strike one” but that he’s not going to punish me since I was given the wrong address. He asks the scheduler “do you have anything to add” to which she replies (and this isn’t a direct quote, but something to the effect of) ‘I don’t like that your hair is curly. You should brush your hair every day. It’s unprofessional for your hair to look like that.’ I should clarify, I’m white, but I have very very curly hair due to a Hispanic grandparent and some others in my family tree.

At the next “meeting” I was asked by my boss and HR if I plan on staying long term or not because they are “investing a significant amount in my training” (I haven’t received any training on my units yet). This meeting was pretty uneventful besides me telling my boss that the scheduler made me uncomfortable with her comments about my hair, to which I was told she was a “mother hen” type character so I shouldn’t worry much about it. However, I found out later from my tech supervisor (who I have become friends with and also was in the meeting) that the scheduler has been trying since day one to get me fired and that he’s been trying his best to have my back with the bosses. This was news to me and I have no idea why she has it out for me. Apparently, she tried to use me leaving early a lot as a reason that I should be fired, BUT SHE WAS THE ONE WHO WAS TELLING ME TO LEAVE EVERY DAY.

I just got an offer for 7 more dollars per hour at another job as a tech at TEL. I’m very much considering taking this job, but my two questions are as follows:

How do I go about politely leaving after JUST telling my boss I was planning to stay a while?

Has anything illegal or inappropriate been done to me by the scheduler or employer??

This is my first civilian job since leaving the military. I’ve done nothing out of the ordinary, I get to work on time, and do as I’m told without question. I’ve gotten all my basic trainings done ahead of schedule, and get work and paperwork done quickly and efficiently.