I agree with what others have said about driving.

It is a good 5 hour drive from AMS to FRA without traffic and given that you will be driving through some of the most heavily populated areas in Europe, then you can expect traffic in most cases (Sunday morning is probably the best time to drive!), And if you are unlucky and drive through rush hour or get stuck following an accident or two then you can add a good 1 -2 hours onto that figure.

I would suggest to either take the train (there are several direct trains per day which I think take about 4 hours) or Fly. Although there are no direct flights by LCCs between these two places. But you can often get good deals with both KLM and Lufthansa if you book in advance and are flexible with times/dates.
If you want a car at either end for whatever reason, then it is best to just do a couple of separate hires.

If you do decide to drive however, then one diversion that is worthwhile could be to drive along the Rhine between Koblenz and Wiesbaden/Mainz. You can drive either side of the Rhein (B9 or B42) but just be aware that there are no bridges between the sides, but there are some ferries. The drive/trip through this area know as the Middle Rhein is very beautiful and you won't be disappointed. A stop-off in the Loreley is also worthwhile (google it!).

If you take the train, then you can also follow this route along the Rhein but this would require changing in Cologne, and then taking a different train which would go via Koblenz and Mainz (where you might have to change again). So it would take much longer.