Netherland and Belgium with Flexible Plans

Amsterdam you would just take the train from Rotterdam to the center of town and walk everywhere since it is so compact. You could cover Haarlem on the same day by train first.
You or someone in your party just needs a smart phone or tablet with google maps (not necessarily a paper map) and internet access to get around to all where you want to go. I often map things out on my tablet weeks before I get there and save it.

Since you are renting a car you should get a guide book and they usually have maps and research on the Netherlands and go to the places that interests you more spontaneously outside of Amsterdam and Haarlem;

Trip length is four and half days. As an experienced traveler, I
realize that’s a short period, but it’s a post Rhine River cruise
thing. We are looking at doing a vacation rental and staging out of
Rotterdam for day trips. The minimalist plan includes: (1)-
Rotterdam (2)- The Hague (3)- Amsterdam (4)- Haarlem (5)- Antwerp

So you are planning to see five cities in four and a half days? Even if distances in Benelux are short, that still sounds very optimistic and you will not see much of them.

I will be renting a car, but train and bus will be individually
considered when more convenient.

Why? The Netherlands is probably the least car friendly country in Europe and it has a great network of trains and buses.

I am comfortable with driving most any place in Europe – on both sides
of the road. I understand that Amsterdam traffic will be bad.

As someone wrote in another thread about cars in the Netherlands "It is a burden in Leiden and a horror in Amsterdam city". Don't drive in Dutch cities, they are designed for people, not for cars. It not so much a question about bad traffic as of narrow streets with plenty of one way streets and bikes everywhere (and they are fast). And paying €8 per hour or so for parking.

one needs to drive like a Kamikaze when in the roundabouts.

Please don't do that, you will be hated by the locals.

I like the convenience of a hire car because it is a DIY thing that
allows a deviation to the “plan” whenever we wish.

Nothing stops you from deviate from your plan if you go by train. Dutch train tickets are not bound to a specific departure, so if you see a nice town along the route, just alight and continue the trip with the next train.

When in England we found parking lots on the outskirts of larger towns
where you could get on a public bus and ride into that town.

There are park and ride parkings at many smaller railway stations in the Netherlands.

Your OP contains all the reasons why you don't need or want a car. I've been to Amsterdam at least five times, and I've always visited at least two other cities while there, by train. I've spent many weeks in Antwerp, and the train is by far the best means of transport there.

Just one example, it takes half an hour to get into a city and drive to the $20 a day (at least) parking garage, and to get out of town afterwards. Do you have time to waste on this overhead for each city?

Tim> Thanks for the info about the cost of parking. I've only got about 6 hours to do Antwerp. I am wide open to suggestions on what to see/do.

Jazz+Travels> Fantastic idea about tablet maps. Thank you so much!!

Badger> I stated in my OP that I was not a neophyte in driving all of Europe. This is not my first rodeo doing that. I can do it as well as the locals. I appreciate your observation that I have an "optimistic" plan. It is, but it's what it is. I'll adapt as needed. Respectfully, it has been my experience that trains go in a straight line from point A to B. Having a hire car provides the luxury of veering off at a 90 degree angle. Thanks you for the info about the park and ride lots.

floris> You apparently didn't get the humor in the kamikaze joke and may have the misguided opinion that roundabouts are safer than 4-way intersections. Regardless, I could have done without your sarcasm. Have a nice day.