If you do need the car, have a look at Sixt. They always have a number of German-registered vehicles at Schiphol, so are clearly used to cross-border traffic, and may have less expensive international drop-off fees.
Failing that, the ICE from Duesseldorf to Amsterdam is a very civilised way to travel, and costs €29/adult when booked in advance (
www.nshispeed.nl).