Rehire Eligibility Letter

So to give some background information: When I first graduated high school I became a CNA and started working on a med/surg unit at a hospital. When I was first originally hired, I told the manager that I would be starting nursing school soon and that it was my top priority, so if she couldn't work with my school schedule then not to hire me. Within my first two months of working there I got the flu and had to be out for 2 days. When I returned I had a doctors note and she called me into her office and told me that "a doctors note does not excuse you here". So then it came time for me to start school and at first she was working with my school schedule (which I provided her with a month in advance), then as things progressed she started scheduling me for days I had classes and I would have to call her to get it sorted out. Well she continued to do it and she stopped answering my calls and emails and one time she even responded to one of my emails said that she would take care of it only to call me the day she had misscheduled me to yell at me when I told her that she responded to my email she said "well i dont remember that so im gonna consider this a no call no show". The last and final time she scheduled me on a day I had class she called me while i was in class and asked me where i was and i told her that i was in class and that i had been trying to reach her for a week with no luck. She then told me that if i didn't show up to not call or show up ever again because i would be fired. So i said okay and hung up the phone and didn't think anymore of it.

I am now a RN and I recently applied to a job at the same company, and did not get it. I was really surprised that I did not get it because I over met the qualifications and the position still hasn't been filled. That's when I thought of that incident so i called HR who informed me that I am marked as "ineligible for rehire". However, the lady said that I can write a letter to the DON and explain the situation and then she can decide whether or not to make me eligible for rehire again.

So the reason for this incredibly long post is for some advice as to how I should go about writing this letter. I'm not sure what to include or whether or not I should apologize or exactly how to compose such a letter.

I know many people would just say to forget about it, but I happen to live in a small town and this is the only health system in my town. Also, the available position is my dream job.

Any advice would be greatly appreciated! Thank you!