How are the pets traveling? If the pet is traveling inside a cage or carrier, it may be easier for the kids to care for the than if they are traveling another way. Pets can get agitated during traveling. Usually, this behavior will occur in cats or dogs. Those contained inside a carrier may be easier to control. Small animals, like hamsters, guinea pigs, and rabbits should be traveling in a cage. They cannot run loose around the vehicle. Not only will they be harder for kids to handle that way. But they will also not be safe at all.
What size are the pets? Larger pets are better cared for by the adults during a road trip. This is because you never know what an animal will do when frightened or agitated. Your pet may be perfectly fine and not have any reaction at all. Then again, exactly the opposite can happen and you don't want your child to be on the end of that. Large animals should be secured safely in the proper travel restraint. Small animals are likely to be in their cages. Therefore, they are not likely to be a direct threat to your child.
Can your child calm the pets? If the pets are easily soothed by your child, it may be a good idea to have them somewhat near your child on the trip. Again, consider safety. But as long as your child and the pet are safe, there is no harm in your child using soothing words to ease the pet's fears. A cat or dog may be easily calmed by hearing your child's voice or by your child petting his fur.
Who's in charge? The kids or the pets? This is very important. Does your dog or your child normally run the show? If it's the latter, it will be very difficult to calm and care for a pet during travel. In this case, this is not a responsibility for your kids to take on. On the other hand, if your child is very good at controlling the animal's behavior, safety may not be an issue in that area. In that case, it may actually be a good thing for your child to care for the animals during the trip.
Is your child really responsible enough for this duty? Road trips are stressful for kids as it is. Some kids can handle the extra added responsibility of one or more animals. But others would be better off leaving that up to the parents. Pet care during a road trip can be a great lesson in responsibility. But it's only a good idea if you know that your child will be a positive influence on the animal's behavior, as well as tend to their basic needs. While parents are focused on the road, kids with this task will be checking on the pet's water, food, waste elimination, and other needs. If your child already handles these kind of duties at home, it will be easier to catch on to proper procedures during road trips.
*This advice is based on the author's personal experiences and is not meant to replace that of your veterinarian or pediatrician. Always ask licensed animal care specialist about your pet's specific needs. Always contact a licensed pediatrician about your child's health and care.