The quarry is really interesting, my kids, and later grand kids really enjoy it (me too)
I really like the Tilted Rock self guided tour. The road starts at the Quarry. If you purchase one of the guide books it tells about each stop at various pictographs, petroglyphs, and geological formations along the route. Some are an easy walk, some require a bit more hiking. Make sure you bring water, sunscreen, etc, this is a high desert area. At the end of the road is Josie Bassett Morris's cabin. She lived there from 1913 until 1963 in a cabin, she built herself. The last few miles of the the road are unpaved, but usually maintained. The tour is well worth the time if you are interested in that kind of stuff.
As pets are restricted in/on some of the hiking trails as well as the quarry buildings, plan for that.
The only issues I ever had was being a newbie pulling a 16 foot pop-up trailer with my full size work van. I was a bit challenged parking in the loop at the end. Backing with surge brakes, figuring out what my spouses wildly waving hand gestures while backing up took some getting used to.
My last trip there, July 2015, we actually camped at Steinaker State Park, Utah and drove to the quarry and tour from the campground.
Tour of Tilted Rocks - Dinosaur National Monument (U.S. National Park Service)
Josie Bassett Morris - Dinosaur National Monument (U.S. National Park Service)
Quarry Exhibit Hall - Dinosaur National Monument (U.S. National Park Service)