I wouldn't try letting her out on a harness. A friend's family did that and the cat was so freaked out she wiggled out and got away. They were actually able to find her (several hours of driving back and forth on weekends with flyers and stuff).
Anyway, keep her crated in the car and bring extra towels for the crate in case she has an accident in there. When at the hotel at night, keep her either in a big dog crate with her litter, food, water, and bedding or in the bathroom with the door shut. Just having her in a separate hotel room may not be enough-many cats will try to make a run for it. Actually, most cats have a "different" personality when stressed; you can have hand-raised kittens take on feral attributes and feral cats so scared that they'll actually sit still for you to pet them. You never know how cats will react in new surroundings unless you've been there/done that with them before (and even then, they may just surprise you).
When you get to the new house, aside from having your stuff around to comfort her, I would keep her in a certain bedroom (preferrably yours or a child's-whomever she's most comfortable with) for a week or so. It makes them more comfortable. It all depends on the cat, of course-I have one that thinks, within five minutes of being somewhere, that he must live there now, so oh, well, might as well claim his spot on the couch. He's weird, though (he can go to petsmart with me and be fine-I think he was a big, lazy dog in another life-he's less territorial than a cat and more pack-oriented like a dog almost).
I've transported cats many, many times (I used to be very active in rescue, particularly cat rescue). If you have any questions, feel free to pm me.