Lynn, there is no town spelled "Uhdenhausen". There are, however, two towns spelled "Udenhausen" (no "h"). The problem is that neither one is located in what was until 1866 the Duchy of Nassau (capital: Wiesbaden).
One Udenhausen is located in the former district (in German: Kreis) of Hofgeismar in what was until 1866 Electoral Hesse (in German: Kurhessen), the capital of which was the city of Kassel. From its capital city, Electoral Hesse (Kurhessen) was often referred to as Hesse-Kassel (or to use the older spelling, Hesse-Cassel).
In 1866, the Kingdom of Prussia (in German: Preussen; capital: Berlin) annexed Nassau, Hesse-Kassel, and the city of Frankfurt and combined the three territories into what was to then remain until 1945 the Prussian province of Hesse-Nassau, with the city of Kassel as its capital.
This Udenhausen is today part of the town of Grebenstein.
The other Udenhausen is located the former district (Kreis) of Alsfeld in what was until 1918 the Grand Duchy of Hesse-Darmstadt, the capital of which was the city of Darmstadt. Following World War I and the abolition of the German monarchies, Hesse-Darmstadt became simply the state of Hesse, but with borders completely different from those of today's postwar state of Hesse.
This Udenhausen is today part of the town of Grebenau.
Following World War II, most (but not all) of the Prussian province of Hesse-Nassau, and most (but not all) of the 1919-1945 state of Hesse (the former Hesse-Darmstadt) merged to form today's state of Hesse (in German: Hessen), with the city of Wiesbaden, Nassau's former capital, as its capital.
So what it boils down to, Lynn, is this:
If you are absolutely certain that the Schaefer and Heine families were from a town called Udenhausen, then you are mistaken about their having been from Nassau. If, on the other hand, you are absolutely certain that they were from Nassau, then you are mistaken about their having been from a town called Udenhausen.
From what kind of a source -- that is, what kind of a record or document -- did you get "Uhdenhausen, Nassau" from?