One way, cross-border rentals in Europe are possible, though very, very expensive. And for all practical purposes, Hertz, Avis and company all are companies doing business in Europe, nobody cares who owns the shares of the mother company. You'd have to contact the rental company in Amsterdam to ask for prices and other details.

As for the leisurly drive from Amsterdam to FrankfUrt through the countryside, yes, this is possible, but unless you carefully plan your itinerary, you're in for an unpleasant surprise. You're talking about one of the most industrialized and heavilly populated areas in the whole world. Perhaps a better (and possibly much, much cheaper) idea would be to fly to Amsterdam, visit for a couple of days, fly with a LCC to FRA, get a rental car at the airport and do 4-5 days in Germany before flying back to AMS to connect to the flight home.