Apparently the confusion over how this name was spelled -- BUDDENBERG or BUDDEBERG -- wasn't limited to American records; baptisms from the Lutheran church in Rödinghausen go back and forth between the spellings.
I extracted information for eight BUDDENBERG children, four each from two families. The priest's abbreviations for writing town names makes it unclear exactly where Johann Friedrich BUDDENBERG's family lived, but they weren't the focus of my search anyway.
I was looking for the baptisms of Johann Heinrich BUDDENBERG's children and I think I've found the proper town names for "Schwend." and "Donoh." "Schwend." likely refers to the town of Schwenningdorf, a couple of kilometers southeast of Rödinghausen. When Johann Heinrich's fourth child was baptized, their residence was listed as "Donoh." The town of Dono is a couple of kilometers east of Schwenningdorf.
The baptism records did not end the confusion over Johann Heinrich's wife's name. None of the four baptisms list her full name; the most that was revealed was "Cath. Mar." I think it's safe to assume her name was Catharina Maria, or Cathrine Marie as one entry in the IGI cites. As for her surname, the records alternate between SCHALE and SCHOLLE.
There was no indication as to when or where Johann Heinrich BUDDENBERG and Catharina Maria SCHOLLE were married, so for the time being I'm going to assume it was at Rödinghausen and order the microfilm for marriage records at some point for verification. This may turn out to be another four- or five-roll order to track down all of the baptisms, marriages and deaths for this family.