If it's Tuesday, this must be Belgium.
To each their own, but I think you're trying to do too much in too little time.
You have 4 x 24 = 96 hours. If you manage to drive non-stop, that's at least 15-16 hours (I checked Google maps, but that's assuming you won't get stuck in traffic.
You'll also have to sleep, eat, find a spot, set up the tent, and put it away again the following morning. Even if you do everything very efficiently and sleep short, it'll take about 8 hours out of every 24. Not counting the nights before and after, that's 3 x 8 = 24 hrs. So that leaves you with 56 hours — for 13 cities (not counting Amsterdam).
That's four hours per city and no time to spare.
So what do you want to do? Get out of the car, walk around the city, take a picture to prove you were there and drive on?
What I would do if I were you, is focus on Amsterdam and everything that's doable with a day trip from Amsterdam.
First of all, there's Amsterdam itself, with the big three museums: the Rijksmuseum (Rembrandt, Frans Hals to name but a few), the van Goghmuseum, and the Stedelijk (City) Museum (modern art). That's a day at least.
Then there's the Red Light District, the almost obligatory boat trip through the canals, or alternatively, a bike tour. And that's just focusing on the main tourist attractions.
I you decide to visit Brussels, that's doable as a day trip by train. Brussels has a number of things to see and to visit, including Manneken Pis, the Atomium, the Comics Museum, the Museum of Natural Sciences (featuring the largest group of Iguanodons ever found). That's more than enough for a day.
Going back to The Netherlands, there are day trips to The Hague, where you can visit the Gemeentemuseum (City Museum) for the Mondriaan paintings, Madurodam to see The Netherlands in miniature (that probably will suit your need to see as much as possible as fast as possible), the Vredespaleis (Peace Palace), Panorama Mesdag, Escher in the Palace; more than enough for a day.
Other day trips could include Volendam or Urk (authentic fishermen's villages), the Openluchtmuseum (Open Air Musuem, where historical buildings have been transported to, to show you live in 'ye olde times'), the Afsluitdijk in the north or the Delta works in the south-west.
But by staying in Amsterdam and day tripping, you'll lose less time then when doing a roundtrip by car.