I just took my bunny on two 4-hour car rides this past summer a week apart and she did well. Well… well enough. She did go through bouts of stasis each trip, but it’s hard to say if it was the car ride or her medicine since I had started her on antibiotics just prior to the drive each time.
I do what Little Lion Head does and keep her in a small cage (so she’s not sliding around and hurting herself, a small cage is a bunny seat belt) on the floor of the front passenger side so she could see me and I could see her and make sure she was doing alright. I had her harness on her in the cage so I could clip her leash on and get her out in case I needed to. On the first 4-hour trip I stopped halfway and let her out of the cage and sat with her on my lap to calm her down, let her eat, and use her litter box. She did much better on the second trip and ate hay the whole way home and was generally much calmer.
When you go to your parents, I recommend bringing his favorite treat, or even a bag of Critical Care in case he does stop eating from the stress. Keep a CLOSE eye on him for the first few days, especially when you first get him there, and make sure he’s eating. Worse case scenario, what I did with Meki was I mashed her pellets into a powder, added water to make it a paste (essentially home-made Critical Care), and put it into a bowl and let her lick it off my finger until she licked it out of the bowl herself.
If you can, to get him used to the car, give him short rides here and there, gradually getting longer, leading up to when you’re going to take him. Start off with maybe 15 minutes and gradually make it longer rides.
I heard putting a carpet square under his cage can reduce the bounciness of the car ride, and try to attach his water bottle to the cage somehow with some fresh hay for him to nibble if he can.