Exempt means you get paid no overtime, and get paid a set salary regardless of the hours you work. You MUST have certain responsibilities like overseeing other employees. Be sure to check to see if the position meets those things. Many employers have tried to make employees exempt with-o giving them any of the responsibilities/freedoms that are specified by law. Non-exempt means if you work over forty hours, or on certain holidays, you get paid extra. You cannot have hiring/firing responsibilites, etc... and you get paid based on how many hours you work.
Hope this helps. Seems like the new position has a lot of things that are not explained. How is the job going so far? I hope as you settle in you find you love the job. I also hope that the court system for difficult child is a lot better in your new area!
