If your plan is to exit DV park to the southeast (into Baker) and head to JT from there, I'd highly recommend passing through the Mojave Preserve. You can take Kelbaker Road from Baker to Kelso and check out the old train depot that is now the MNP visitor center. On your way into Kelso from Baker, you'll pass by several cinder cones and have a great view of the Cima Dome to your north. The depot is really cool, and if you enjoy the history of the area, you can easily spend two hours there going through all the rooms and checking it all out. There used to be a small restaurant/snack bar inside the building, but it went out of business a few years ago when the operator retired. The tables and chairs are still there, so you can sit and enjoy the AC while you have lunch that you bring yourself.
From Kelso, you can continue south on Kelbaker Road and, if you wish, you can stop by the Kelso Sand Dunes about halfway between Kelso and I-40. The dunes themselves are a wilderness area, so you can't drive right up to them. There's a parking area and trailhead, and it's just a short hike to them if you want to see them up close (a half mile or so each way), but even the view from the parking area is pretty impressive if you just want to make it a quick stop. You can continue south on Kelbaker, past I-40, and turn right (west) on Route 66 and stop off at Roy's in Amboy for a delicious Route 66 "Route Beer." Stopping here for a root beer is one of my favorite things to do in the desert. More than once, I've driven all the way out to Roy's just to sit there, drink a root bear, and watch trains pass by in the distance as I take in the desert scenery.
Again, if you're looking to get out of the car and stretch your legs, the Amboy Creator (right down the road from Roy's) is a pretty cool little hike. It's about a mile and a half each way and there's only a couple hundred feet of elevation gain, all within the last tenth of a mile as you climb the side of the creator into the volcano. The desert views from the rim of the creator are great, and you can check the "been inside a volcano" box on your bucket list.
It'll take about 2 or 3 hours to hike to the rim of the creator and back, so this is another one you may want to skip if you're just passing through.
From Amboy, you'd take Amboy Road south into Wonder Valley. At that point, you're just outside the Old Dale district, but your best bet would be to head west a little further into Twentynine Palms for some gas and other necessities. There are plenty of hotels in Twentynine Palms if you wanted to rest one night in a real bed and have a shower. Plenty of restaurants and fast food here as well. From Twentynine Palms, you'd head southeast into the Old Dale Mining District and into JT from there.
Without the hikes, this would basically be a full day with the stops at Kelso, Roy's and Twentynine Palms, ending the day in the Old Dale Mining District (or ending in Twentynine Palms and starting your next morning in Old Dale, if you choose). Enjoy the trip, sounds like it'll be a blast!