Renting/Driving a Car in the Netherlands

The issue is that we want to visit a niece who studying at a private
school in Maastricht. (two hours by car, three hours by train)

Driving from Amsterdam to Maastricht in 2 hours is very optimistic, if not impossible, if you are obeying the speed limits. The overly optimistic Google maps says 2:15. On the other hand, the fastest trains do it in 2.41. So I think the trains are the fastest way. Especially when you factor in that picking up a rental car usually takes a lot longer than buying a train ticket.

So, is there a better way to do this? Can this be done without renting
a car?

Yes, public transport in the Netherlands is easy to use and the network is dense. Apart from Giethoorn (that will require a bus ride) it can be done by train.

My wife was hesitant to rent a car, because she said the road signs
would be in Dutch, and we don't speak Dutch. But I will learn the
European road sign markers and with Google Maps, Apple Maps and a GPS,
I will be on major highways/tollways? and don't anticipate I will get
lost.

Of course any text on the road signs will be in Dutch, but the road signs follow the Vienna convention so they look more or less the same as all over Europe. And are to be honest not that hard to learn.

I am more afraid of the inner city driving and driving into areas
where cars are prohibited and I don't realize it. Or how to park in
the city center, if you need to put a pass in your windshield, etc.
etc.

If you have been to the Netherlands before you must know that Dutch cities are built for people and bikes, and not for cars. The best advice for inner city driving is: Don't do it!

Instead of driving from Amsterdam’s Schiphol Airport, I would take the train to Maastricht instead. This requires a connection in Hertogenbosch (1h 15m) and continue on to Maastricht (1h 30m). You don’t want to drive in a foreign country after being up all night.
You can take a train from Maastricht to Almere, but that too requires a connection taking a total of 3h. To get to Giethoorn from Almere, you can take a train from Almere Centrum to Steenwijk (1h 15m) and transfer to a bus to get to Giethoorn (15m).

I should also add that if your first stop is Maastricht, Schiphol is not necessarily the best airport to fly to. Düsseldorf, Brussels or Frankfurt are other options worth considering.

It isn't clear to me that derek is landing and then immediately heading off to Maastricht. I read it that these 3 days were in the middle of an Amsterdam trip. I think they are starting from Amsterdam and want to get the car for the road trip at the airport to avoid driving in the city.

If they had just flown in would they they drive for 2 or 3 hours?

Starting from Amsterdam the hourly train goes directly to Maastricht having only started in Haarlem so unlikely to be late.

On the driving questions:

she said the road signs would be in Dutch, and we don't speak Dutch.

Like most European road signs they will be pictographs. Learn those. The names of town will be the same as they are in the map. You don't need to speak Dutch to drive in the Netherlands. I speak a little but from day 1 I've never had any problem. You do need to think in kilometres. Figure around an hour for 100 km on major highways in Europe, a little less in Netherlands because of the congestion and the generally low speed limits in that country.

/tollways?

There aren't any.

I am more afraid of the inner city driving and driving into areas where cars are prohibited and I don't realize it.

Valid concerns. Become familiar with the square sign with playing children and understand clearly its meaning.

Or how to park in the city center, if you need to put a pass in your windshield

Street parking is rare, free street parking is hen's teeth. Certain areas is for residents only. Don't try - use parking facilities. Expensive but straightforward. Spaces and driving inside the car park can be quite narrow. In small towns you can use a parking clock for a short period in clearly marked certain areas.

Will I need a vignette or pass to drive in certain areas or motorways? in tollways, how does one pay for tolls? Is there an E-Z pass (electronic) device, I should get as part of the car rental?

None of that in the Netherlands. Not an issue.

Is there something peculiar or special to driving in the Netherlands that I am missing?

The speed camera was invented in the Netherlands and the country is absolutely crawling with them in all their many variations. Don't speed at all - they WILL get you and you will be poorer.

Also, as mentioned earlier, you may be surprised by the density of cars. Leave plenty of room. Be prepared for Belgian and Luxembourgian drivers as you make your way through the Dutch Alps approaching Maastricht. They have their own techniques some of which will set your teeth on edge.

Don't undertake (overtake on the wrong side). Study the symbols. Again.

Happy travels...

Great information from all! Don't worry, folks. We'll be in Amsterdam for 4 or 5 days taking in the sites, before we make the trip to Maastricht .
I would never drive a long distance right after a long flight. In fact, we always come arrive a couple early before we take a cruise or a tour just to get over jet lag .

The only reason I mention getting and returning the car at Schipol is that I don't want to rent a car in the center city area and have to drive my way out of it. It just seemed that renting outside the city center and at the airport would give me a clear shot to the A4, then the A9 and then the A2 to Maastricht.

I suppose we could train to Maastricht and then take a taxi to her dormitory. and take a taxi to take our niece out to dinner. But with a 3 hour train return ride, it might be best to stay overnight in Maastricht before heading back to Amsterdam.

Still not sure what to do. Any other insights are welcome.

Thanks for the clarification! I misunderstood and thought you where heading to Maastricht direct after landing at Schiphol.

But, in that case the trains is the much faster option to Maastricht. By train it is 2:25 from Amsterdam centraal to Maastricht, + maybe 10-15 minutes by city bus to wherever your niece lives. 2:40 or so altogether. By driving it is first train to Schiphol (15 min), collecting a rental car (15 min?) and then drive to Maastricht (2:30-3h). The same with Almere, the train from Almere to Amsterdam is much faster than driving to Schiphol, returning the car and then taking the train to Amsterdam.

I suppose we could train to Maastricht and then take a taxi to her
dormitory. and take a taxi to take our niece out to dinner.

Or just a regular city bus?

But with a 3 hour train return ride, it might be best to stay
overnight in Maastricht before heading back to Amsterdam.

I think that is a good idea, 2:25 is a bit too long for a day trip in my opinon.

and it gives you time for a second koekje with your niece who you have travelled so far to see...

I support MaryPat’s remark getting to Giethoorn. Get there as early as possible before the crowds arrive. With Covid my visit last week was very doable, not so much visitors. According locals unique, it can be a complete madhouse there. And Maastricht is nice enough to spend a night there.

I have never felt that it was a particular problem to pick up and drop a rental in Amsterdam. It's actually a convenience to be able to do that. As has been noted hear, the public transportation in the Netherlands obviates the need for a car but as you well know, a car does open up many convenient possibilities. GPS takes much of the agony out of driving in big cities.
If I were planning to have a car I would make sure that there is available parking wherever you stay. Expect to pay for it. The convenience of hotel hotel parking cannot not be overstated and is well worth the fees..

For visiting cities public transport in the Netherlands is usually (as already noted) the best way for moving around. Nevertheless considering a car remains not a bad idea too as in some cases it can bring you to places you would skip otherwise and so making the trip more worthwile. But consider it from case to case, to see if it really pays off.

For instance a visit to Giethoorn can be much more interesting combining it with a scenic drive. Staying in Almere you can drive to Emmeloord along the A6 freeway and turn off to Steenwijk / Giethoorn. Blokzijl is lovely for a stop. After visiting Giethoorn you can drive for instance south to Hattem near Zwolle and after that you can continue along the leftbank of the river IJssel to Deventer. There is a parking (De Worp) at the leftbank next to the foot passenger ferry. Further south Zutphen has an even more beautiful historic centre.

Back to Almere Elburg is worth a detour. This is just an example, hopefully your hotel in Almere has more suggestions.