If it fits in the car why not? You said you have room in the rental place, so why sit there and wish you had it with you? When we go anywhere for any length of time and are driving I take a machine. My husband used to try and talk me out of it, am I really going to use it? Then he took his bike a couple places and never got on it, so never says anything about it because if I have time, I sew. My sewing is very relaxing for me and it sounds like that is the same for you.
My only concern would be, since you are driving, it is going to take a few days to get there. Do you want to lug it into a hotel every night?