How should I handle this situation with an employee?

Here is my situation. I have been with the same company ten years, had been the Staff Accountant all this time, and just got promoted to Assistant Controller when the old assistant controller, Tom, left. I report to the Controller, and I have an accountant, 2 A/P people, and 3 A/R people reporting to me. I have never supervised anyone before. I have been having issues with one of the A/R people, Donna. Tom was a nice guy, but was a little too easygoing with Donna. I'm not sure if he was afraid of her for some reason, or just didn't like confrontation. She used to take off at month end, knowing full well no one in the finance department is supposed to take off at month end, also knowing Tom would not tell her no, and the other 2 A/R people would be furious that they were slammed because Tom was afraid to tell her she couldn't take off at month end. She wanted to take off at month end the a couple of months ago, and I told her, "No. It's month end." She went over my head to the controller, who backed me. The other thing is, the 3 A/R people take turns going to the bank during the day with the deposits. When the other 2 A/R people go, they're back in 20 minutes. When Donna goes, she is gone over an hour. Tom used to comment about this all the time when she was gone, but would never say anything to her. The other day, I politely told her, "You shouldn't be gone over an hour when you go to the bank." She replied, "Then I won't go anymore. It's not in my job description. I can go to HR." Am I wrong here? I don't think I am being unreasonable saying she shouldn't be gone an hour when everyone else is back in 20 minutes when they go. No one else has a problem going. If going to the bank isn't in her job description, would she have a case against me? I think the thing is she iis used to Tom letting her get away with everything. I'd appreciate any advice anyone could give. It's a bit tough because I never managed anyone before. Sorry for the length. Thanks.