I’ve done the Eastern Shore-Raleigh trip a TON - and usually with at least one dog in the car. I usually figure about 6 hours with a stop.
My two favorite stops are the Bowling Green Exit off 95, just north of Richmond (cheap gas) and the South Hill, VA exit on 85 (good gas prices and a Bojangle’s).
Neither has a great “dog walk area”, but both have food and gas, and enough grass that I can give the dogs a quick chance to drink and pee.
As far as human potty breaks, you know you’re going to need them - so do what you have to do. If at all possible, park in the shade, and be quick - I’m hoping that Blue will be traveling in a crate, so give him some cold water, and drape the crate so he won’t be in the direct sun, while you’re taking care of your business - as much as I hate to leave a dog in a car, sometimes it’s necessary (especially with a 6 year old!), so just be as fast as you possibly can.
Given that it’s going to be hot, I’d do drive-thrus for food, but you don’t have to eat while you drive - find a shady spot and have a little “carside picnic”. (I think the MickyDs at Bowling Green may even have picnic tables outside… and there is a Sonic at the South Hill exit, which might be a good place to take a little driving break.)
For safety’s sake, make sure that Blue is in a well-fitting collar with ID of some sort attached and, if it’s possible, leash him up BEFORE you open car doors. If he’s of the spooky persuasion, you might even consider having him wear a choke or martingale collar to minimize the chances of him slipping his collar if he gets scared. (I know that might not be a popular idea, but there are few things that scare me more than the thought of losing a dog in a high traffic area.)
Traffic on 95 around Kings Dominion/Doswell is probably going to be nasty- holiday weekend and all, unless the weather is bad (so maybe hope for rain?)…
I can’t imagine that you’ll need to stop somewhere and spend the night, but this website: http://hotels.petswelcome.com/ has listings, if that helps. Generally speaking, Red Roof Inns and La Quintas are usually dog friendly, in my experience.
Good luck, and have a safe trip!