Budgie travel

That is a long drive :O It is better to give someone you know to take care of your budgie while you are out, safer for budgie and you avoid his unnecessary stress. If you don’t have any, maybe hire someone to take your budgie, pet store, etc. Then traveling with a budgie, make sure to cover his cage to avoid stress, give him enough food and water. but as I said, try to avoid unnecessary stress.

my female budgie looks different

I think that means that is a hormonal change, she is in the breeding season, ready for mating. I think there is nothing you can worry about, except if gets larger to cover her vents for breathing, then get her to the vet. You should never breed blood siblings. Read more here https://alenaxp.com/can-budgie-siblings-mate-breeding/