We do that often, and I wouldn't worry about that. Our issue is fitting it all in the car, but we get creative! Kids have case of water under their feet in the back, maybe something on their lap, etc...
I've done it where we checked in, then I ran to Target first day. I was like the walking dead in the store. Laughing, I told the check out lady that I had been up nearly 24 hours and it was like midnight to my body! That was a trip that we just took carry on bags, so didn't even pack things like shampoo & toothpaste, so I was picking up toiletries and drinks & breakfast food to get us through the first day. Then the next morning DH and I made our first big Costco run right when they opened.
I agree, you will likely want to settle in and relax, so to me it's safe (and I lived on Oahu, so know other than what you're talking about, no we don't leave anything valuable in our car ever). Only thing we do leave is if we go out for the day, we usually have a small soft sided cooler with bottled water in it. Not worth anything, so that's fine in the car. Especially when we go to the flea market, we are hot and thirsty!