We always use www.autoeurope.com

What site are you using to find your train fares and when are you travelling.

Dont forget with renting a car you need to be over 25 (or pay a fee for young drivers), pay for gas which is MUCH more expensive in Europe, pay tolls for the road, pay for parking...

You will also need to drive through the cities and understand their rules of the road.

There are also usually hefty (several hundred euros) fees for picking up in one country and dropping in another.

Taking all this into account I think it will end up being cheaper and less of a hassle to take the trains.

Picking a random date the cheapest ticket to Luxembourg is €61, using Thalys and changing in Brussels.
Have a look at a Benelux train pass - it may be cheaper, though I don't think you can use Thalys with one.

If you are renting a car you must tell the company the countries you intend to visit. The one way drop off fee could be quite hefty, and is not always clear when you make a booking. Often you have to pay it when you pick up the car.
Petrol in the Netherlands is really expensive, as it is in Belgium. Cheaper in Luxembourg so fill up there.
Parking in all three cities is also expensive, so only rent the car when you are ready to leave Amsterdam.
It may work out cheaper to rent a car if there are enough of you.
Bear in mind you may pay extra for an automatic, and they may not be available.

When are you planning this trip?
The drive from Amsterdam to Luxembourg is long and boring imho. You could maybe break it up with a visit to Maastricht or Liege.
If you are planning a summer visit the road will be very busy.

we usually use www.raileurope-world.com and www.eurorailways.com for trains and eurolines.com for the buses. we are travelling on December 11-18th.

im 26, so no extra fees should be applied.

That is a lot of ground to cover in 7 days, especially if you are coming from the US, and will have to deal with jet lag.

Anyway on December 14th for example you can get to Luxembourg city by train from Amsterdam Centraal for €59.20, but it will take you 6 hours.
Driving will take over 4 hours if you go the fastest route (via Antwerp and Brussels, or nearly 6 hours via Maastricht. Without stops, and will cost some €50 odd in petrol (€40 in diesel), depending on the car.

Daylight is short then (maybe 7 hours of good daylight) and there is a real risk of snow in the Ardennes and Luxembourg. Winter tyres are compulsory in Luxembourg, and your hire car may not be fitted with them.

Unless you have some compelling reason to visit Luxembourg given the length of your holiday I would give it a miss and give more time to both Amsterdam and Brussels, and take the train between the two.

You should checking the countries' national railway websites for fares instead of paying extra to Rail Europe. And yes, that's too much ground to cover in 7 days. You'll spend all your time inside a car or getting on and off trains. I'd definitely skip Luxembourg.

thank you guys for all your replies! i think we will skip luxembourg and take a bus to brussels which is only 9 euro. though visiting more than two countries would be awesome.

I think you will find that 2 places in 7 days is better. You will actually get to see the places you visit as opposed to racing from one place to another - especially given the short days in Dec and potentially bad weather.

Dont worry about trying to cram multiple countries into a trip (especially Luxembourg...) you dont need to visit more countries to have a varied trip, each city will be different so enjoy each one!

If you want to see another lovely town you could do a day trip from Brussels to Bruges very easily.

I think you have made a wise decision to drop Luxembourg from the itinerary.

The train system in Belgium is inexpensive and there are many good day trips from Brussels. I wrote a trip report last fall which describes some of them.

Spend the week in Amsterdam, Have fun with whatever you do.

There are lots of great cities to visit that are close enough for day trips. So you don't have to be stuck in two cities without a car. Plus the trains with in Belgium (the regular trains) are not very expensive.

You could visit Antwerp, Gent, Brugges in Belgium or The Hague or Delft in the Netherlands, for example.

Have fun.