Supervisor bossing me around, I was a manager before this job....?

If the "Bad Supervisor" gets the job you will have to follow his/her lead as he/she will be your boss. Remember you may have experience and knowledge but you are a new part time(20 hrs p/wk) employee. You have only been there a couple of weeks and need to give the job some time. The management team probably hasn't had time to thoroughly evaluate your performance yet.