Travelling by car with children means you'll have to pay twice as much attention to everything and be very, very patient.
Children aren't all alike, and while some fall asleep as soon as they get to the car, others just flat out hate travelling by car and, most of all, being trapped to a chair. Whenever possible you should choose a time when heat's less intense and that doesn't overlap with meals. For quite some families, nap time, for example, can be the best time to hit the road.
For everyone's sake, and independently of tantrums or other situations, the solution must never involve carrying the child on your lap, where he'll be out of his chair or seat and, worst of all, without his seatbelt. If the situation becomes unbearable for the driver, maybe it's best to have a break to tend to the child's needs before heading out again.
Unfortunately, road accidents continue to be widespread and are still the number one cause of death and infant's temporary and permanent disability. As such, prevention is key, and safety is guaranteed by making sure children travel in the utmost safety.
Using children's chairs or seats becomes essential, moreover as it is required by law: all children under 12 years old and 150cm must travel in a chair or seat appropriate to their weight and size. If the baby weighs less than 10kgs, the seat should be installed in the direction opposite of travel.
You can find these and other information in your local Child Safety association.