It's good to reflect Dhamma while driving and be mindful.
Let my person tell a merely personal story:
Once my person was still a householder, a young successful employer, enjoyed to compfortable drive in the "bigges" car of his town, smooth, relacted, V8, no need to push the gas, just driving to the next meeting, 100 of thousand km a year, he got much aware of that * flap * * flap *, on the windows surface on a lonly road.
Reflecting a little more of what is the case of such disaster, he reduced his drives an seeks for more.
Later even took on the bike and focused on work not to far.
After he actually left this all behind, he saw, that if he uses others for a ride, it is sometimes even more worse, so he thought, what if not greed, would one hinder just to simply walk.
Even later, he observed the struggles people have with shoes and how less one in shoes, compfortable, "protective", takes care of his steps. Of course it gives certain freedom to look here and there, but what does one looking for, while under the shoes other are just smashed?
At least, it carries a lot of freedom, if not depending on "protection" and "compfort" and not only that one mostly is much more flexible, much more able to move and even faster as an aeroplain in calculating right, one able to train mindfulness by each and every step, has, if not more, the gain of freedom of remorse made his possession, a liberty not easy to gain, but just step by step.
Of course the "story" is much deeper, but maybe this short cut gives good reason for possible less build on "equanimity" but take on the road of letting go, reduce and sacrifies, step by step.
Maybe some inspirations are also found in some words my person wrote some times ago: Who is the winner in the Traffic of life?.
As for the question again: being mindful on the frames of references, even while driving, is not dangerous but actually good. If it how ever, does not lead to certain insight about the drive behind the drive, does not really lead to disenchantment in regard of having a nice drive, certainly the task might be not right made and can, in this case, be of course dangerous in all aspects.
A nice first step into Dhamma might be also "Step by Step, by late Ven. Ghosananda.
The Buddha called the practice of mindfulness „the only way.“ Always in the present. At this very moment. From moment to moment. In all activity. In this very step.
This is why we say, “Step by Step. Each step is a meditation.” When the children in Providence see me off at the station, as I walk up to the train, they shout, “Slowly, slowly, step by step, each step is a prayer!” and all the passengers look and smile. This saying has become famous!
The children do not know English well, but they know this sentence by heart. They are the new Cambodia, and already they know the way to peace.
In Cambodia, we say, “A journey of 10.000 miles begins with a single step.”
Slowly, slowly, step by step. Each step is a meditation. Each step is a prayer.
If coming across such saying like that of the Batchelors: "You know if a person is really enlightened, when he/she has at midnight a car problem, strong raining and the cell-phone does not work...", than one can be sure that he/she gained the wrong guidance...
[Note: This is a gift of Dhamma, not meant for commercial purpose and other low wordily gains by trade and exchange]