overtime for salaried and hours worked

My wife works for a home health agency in Ohio. She is a salaried employee and does not get overtime. Does she fall under the exempt Status? She was told that the drive to the patient house is not paid time because it was like driving to work. She was also told that her drives between the patient houses in not considered work. She see's between 4 to 7 patients a day. She comes home and works to about 7 or 8pm doing charting and paper work. She works about 10 to 12 hours a day Sunday-Friday and sometimes Saturday finishing up things. She starts on Sunday getting her patient ready for Monday for about 3 hours. She has put in her two week notice and was going to leave before her two weeks was up and she was told that if she did that they would have to put in the system as a no hire for her company and any company that is affiliated with. Is this allowed?