Are you putting him in a car seat or are you holding him? From your post it sounds like you are only holding him while your brother drives. It is against the law not to have a child in a carseat, and you could be harshly fined for not having him in one....even investigated for abuse.
If he is in a carseat, which I hope he is for the safety of all, he probably just doesn't like the restraint on himself. The only thing I can suggest is that you give yourself a little more practice in the car than only family functions. Take him for short rides where he knows that the destination is going to be fun (such as the park) and the ride is going to be short...about 5 minutes. Make sure you don't take him right before or after a meal or when he needs his afternoon nap. Any toddler will be fussy in those circumstances.
Otherwise, dealing with a fussy toddler is a part of life. They have to get used to tough things in life that mean they can't have everything they want, and the sooner they start realizing that, the better.