I think being in his pet carrier for 2 hours will be fine, as long as he has access to food and water and maybe one or two stops. Bunnies won’t usually drink while traveling so stops would be a time for him to hydrate. Two hours isn’t that long so I think he’ll be ok stress-wise as long as the atmosphere in the car is farily chill and relaxed. A dog crate sounds like it might be a bit big for transporting a rabbit…you don’t want him rattling around and injuring himself if there are any sudden stops/turns. There are some good, inexpensive bun-sized carriers on amazon that might work. If that’s not a possibility for you, just make sure to drive carefully and that the crate is secure.
Re: the other pets at your aunt’s house: As long as he isn’t in direct contact with them (which it seems like he won’t be, since you said he had his own room), it’s not too loud (barking or what have you), and none of your aunt’s pets have any communicable diseases they could pass on to your bun, it should be fine. Sounds like you’ve got a great plan.
In terms of prep, I would check and see how much, if any, bunnyproofing needs to be done in the room he’ll be staying in at your aunts. Make sure to bring enough hay/pellets/veg to last both weeks. Also, it might be a good idea to type out specific rabbit care instructions just to make sure there isn’t any confusion about what he’s eating and when/how much. I would also give her the number of your vet as well as the number for the closest emergency animal clinic in case something happens as well as signs and signals of possible illness. Maybe also put down a list of common items that are toxic to bunnies (the HRS has a list I think).
Good luck!