@ghusjil No, she knew how to drive, and she was licensed, such as was required, so your comparison is flawed. Rather, she took out the car without permission in a storm, and nothing more. Of course, neither of those things is good, either, and if nothing else, I'd be ticked that my child didn't have the foresight to either slow down or pull over and wait out the storm. Not that I'd exactly be happy about them taking the car out without permission, either. But a lack of respect and/or trust is something that can be worked on, while suicidal recklessness has a chance of limiting one's future options.
Of course, we don't actually get any insight into where the Duke was at the time, so he may not have actually been able to be contacted. Hence it may not have really been a "without permission", and more just a "without waiting around the house until her parent got back from work to run her plans by them before enacting them". A grey area, essentially, rather than something outright disrespectful or otherwise problematic. On the other hand, she's part of a Ducal household and ended up taking the carriage out without a coachman, so it's highly unlikely she was following proper procedures on the matter, so your assumption on the "without permission" aspect is likely correct.