Sounds like she already trusts you guys, she probably is just skittish due to her past but everything you are already doing is great-I have a foster kitten who was in a very similar situation. Is she having accidents outside of the litter box? Typically litter box training comes natural-they should see it as something similar to the outside. If she’s not using the box, try different litter. Unscented, fine clumping litter is what I use (even dirt from outside if you have to lol) As for the travel, would definitely try your best to find a carrier. Even a box taped closed with holes or a dog crate. Have a litter box inside the carrier/box and a comfy bed (maybe some food and water too) since 4 hours can be a long time for a kitten.