Learning from my mistakes but not sure if this is unlikely

Working in a hospital is the type of nursing I prefer. I have done some traveling, and have been working at a hospital for about 11 months now as a per diem employee. The local hospital is one of the best and well-accredited around. I worked there as an aide 6 years ago for about 2 years, until I got myself terminated for not following through with the paperwork of my leave of absence the right way. I didn't realize the value of being a professional, and I was young and stupid. Now that I've been working as a nurse for 2 years, and seen the difference between a great hospital to work for and a hospital that a nurse would not want to work for. After 6 weeks at a different local community hospital and experiencing a hostile work environment with some of the most unsafe nursing practices I've ever witnessed, I'm regretting the bridge I burned with the hospital I worked for some years ago.

Has anyone ever found themselves in a similar scenario and attempted to prove to their previous employer that they are a changed person? I've been debating over going to human resources at this hospital and explaining this to them, in hopes of a second chance. I'm wondering if anyone else has ever had any luck doing the same?
Sorry that's called the school of hard knocks. I would still check with them and see if you are eligible for rehire since it wasn't a serious offense . It may be worth a try.
There is likely to be a statute of limitations on "do not rehire" records. Most types of HR records have a shelf life of 5 - 10 years. You may want to check on that.