Is it possible that the town where you plan to catch the train is not "Herneveen" but "Heerenveen"?
You say you're going to the Rhine/Mosel... One common gateway for train travel to the Rhine area is the Dutch town of Venlo. There are DB train itineraries from Heerenveen to the Rhine via Venlo, near the border, which can get you all the way to the Rhine towns of Düsseldorf, Cologne, and Koblenz (where Rhine and Mosel meet.) fairly quickly.
Venlo > D'dorf by train takes 1 hour.
Venlo > Cologne by train takes about 1.5 hours by train.
To Koblenz it's roughly 2.3 hours.
So depending on your Rhine destination, it might make sense to take the train directly to the Rhine. Then wake up the next day in whatever your destination town is and pick up your car that day - or on the following day or on some subsequent day, whenever you intend to leave. Fewer rental days is normally a €-wise move.
Closer yet to Venlo is Moenchengladbach (40 train minutes away) where you might pick up a car on that same day of train travel, should you be itching to get behind the wheel even earlier.