Hi!
So I have to travel for at least 3 hours on my breaks (4 times a year)… You should look into a travel cage… they are very small and for a good reason. If you get in a car accident, and there is a lot of room for your bunny to move, then the bunny will slide and slam into the side or other obstacles. With the travel cage, it has enough room to sit up, and to lay sideways/long but not to roam. This way if you are in an accident, the bun is not thrown but simply smushed to the side, which is much safer, and less likely to break bones. (there was a good video I watched..but I do not know how to find it now.). So if the cage you made at home cannot be brought to your school, then buying a cage for at your school and also a travel cage for the trips would be ideal (a big enough cage for the bun to stand on hind legs, lay long, move around, hold a toilet, food and water, and toys). With the smaller travel cage you should take some breaks to give your bun water (although mine wont take anything until it is out of the car) and run around. I have harness’s, but before that we would stop for take out half way and let them roam inside the car until we started moving again. This way you dont have to bring the large cage on your trips.
When I go home my car is packed full of bun things (cages, food, hay, treats, etc.) and a small bag of my clothes, and I have them in the passenger seat in their carrier (buckled in, of course.. however it might actually be safer to put the carrier on the floor because of air bags, which is what happens when I have a passenger). It is quite the chore to load and unload the cage and get it set up in my parents place before being able to let them out there.. It would be so convenient to have a cage at both locations lol.
Good luck!