Mr. Tharp is Dwight's father. It is implied that he divorced with Dwight's mother. He took Dwight's dog in Secret Of The Fortune Wookie. It is is implied that he rather than Ms. Tharp filed for divorce and legal seperation and because Dwight said he used to have a dog (hence the dog door) it is implied that Ms. Tharp and Dwight kept the house and Mr. Tharp got a new one. Another reason aside from private schooling Ms. Tharp might have gotten a new job was to pay off a mortgage on the house because she lost an income source.
One of the halloween stories in the Origami Yoda EU implies that Mr. Tharp is actually the writer of the Origami Yoda series, Tom Angleberger.