I like to think of myself as a libertarian (although those of an anarcho-libertarian bent would probably disagree) and I have no problem reconciling my libertarian principles with this ban.
The central tenet of libertarianism is that you should be free to do what you want as long as you aren't hurting anyone else without their consent. It's for this reason that I think prosecuting adults for not wearing a helmet whilst riding a motorbike or not wearing a seatbelt is wrong. Of course it's for their own safety and they'd be stupid not to do so but if they have an accident and kill themselves they're not putting someone else in danger by doing so. An adult of sound mind is able to make that decision.
Children can't choose whether to get into a car with an adult who is smoking. If they are in a car and the driver lights up they can't demand they stop and let them out. Whilst the driver is perfectly within their rights to smoke in their own car if they wish and in the company of other adults if they consent to being in the car at the same time, any children in the car are unable to consent to having their health put at risk from passive smoking any more than they can consent to sex, piercings, contractual obligations, etc. Children don't have the mental or legal capacity to consent to self harm in the way that adults do and it is proven beyond doubt that cigarette smoke (including second hand smoke) is harmful to a person's health.
Libertarianism isn't about having no rules and nobody telling you what to do, that's anarchism. Banning smoking in cars with children present is protecting someone who can't protect themselves and absolutely compatible with libertarian principles. I for one welcome the ban and hope that the police take enforcement of the ban seriously.