Thanks for all of the replies, much appreciated and great information.
We are 2 adults/2 kids so of course dictated by school but quite flexible as to the actual dates.
After getting blocked in at the parking lot at Mt Rushmore last summer with the dually, we are considering towing a small vehicle for ease of getting around. Of course that puts us in a 40' spot of which there are practically none available for reservation at this point in time for July/Aug. I'll call and see if there's any more availability by phone vs the website but I suspect we just waited to long to make a decision!
Any suggestions on reservable campgrounds outside the park would be appreciated. Considering approaching from the east, then departing to the south. Mostly interested in the geologic features since we are fortunate to enjoy lots of wildlife in our home state camping trips and even in our own backyard! Will look into Grand Teton NP campgrounds as suggested by bka0721.