OK, now it makes more sense. You want to do a drive-through, stopping at the scenic overlooks, walking a short distance, snapping a few pics, get in the truck and drive to the next location. This is what most tourists do, as well as the bus loads of foreigners you’ll encounter. That’s OK.
But if you really want to “explore” as you originally said, you will need more time or slim down your ambitions. I spent 2 days hiking in Grand Teton and 13 days hiking in Yellowstone. And that was still not enough. It’s just incredible, so much to see, but you have to walk and hike to see the best and get away from crowds. Yellowstone is huge with long drives between major scenic areas. Plus you may get caught in traffic jams of cars watching roadside bears, or bison.
I would also recommend you concentrate most of your time on GT and YNP. Plan out your days of travel, lodging, sights to see, hikes to take. Your base lodging could be Jackson, Old Faithful Inn, Canyon Village, West Yellowstone. Or campgrounds nearby. Make reservations. Research what is open and closed. The winters are so severe that there is usually roadway reconstruction every year. Delays happen. Plan it out in as much detail as you can, it will be so rewarding.