Since the ban seems rather limited—it targets a minority of a minority of the population—it's a shrewd way of moving smoking bans into private property and, if passed, you can guarantee that the 'next logical step' will be to ban smoking in the home. This would indeed be logical, since both cars and homes belong to the individual, and children spend far more time in the home than in the car.
The one aspect of smoking in cars that defies the prohibitionists is the fact in a moving vehicle with the window open, smoke is dragged out of the vehicle in a split second. There have been a small number of studies measuring smoke in vehicles and they have only ever found significant levels of secondhand smoke when all the windows are wound up. This is hardly surprising. Nor is it surprising that anti-smoking campaigners only refer to the window-wound-up scenario when pushing for bans.
Consequently, you may hear various claims about levels of smoke in cars being 23 times greater than in a bar, or such like. You may even hear the absurd claim that one cigarette smoked in a car produces the same amount of secondhand smoke as a whole evening in a smoky bar. These myths have all been debunked before, including—in one instance—by the Canadian Association Medical Journal. I didn't realise how much I'd written about this myself until I looked in the archive. Here are the main posts...
On the claim that smoke in a car reaches 23 times the level found in a smoky bar
The effect of opening a window even by 3 inches
ASH's wacky claim that opening the window means that smoke comes back in