It took me all evening, but I've located this family on the 1880 census at 457 Van Cott Avenue, Brooklyn, Kings Co., NY (E.D. 168, p. 713) as follows:
Jacob TREFFASENM W 35 GERLaborerGER GER Pollean TREFFASEN F W 35 GER House Keeper GER GER Albert TREFFASENM W7 NYAt SchoolGER GER
I also located Albert M Treffeisen on the 1930 census at 105 Meadow Brook Road, Hempstead Township, Nassau County, NY (ED 105, p. 5), age 56, with wife Anna, sons Alferd M and Peter living with their daughter Christine and her husband Frederick Wolf.
Although the ages don't fit right for the following family to be the parents of Pauline Reinbolz, they could very well be related:
Brooklyn, Kings (Brooklyn), New York City-Greater, New York, p. 574 Anton REINBOLZSelfMMaleW44GER.TailorGER.GER. Adolphina REINBOLZWifeMFemaleW40GER.Keeping HouseGER.GER. Carrie REINBOLZDauSFemaleW19GER.At HomeGER.GER. Sophia REINBOLZDauSFemaleW13NYAt SchoolGER.GER. August REINBOLZSonSMaleW7NYAt SchoolGER.GER. Charles REINBOLZSonSMaleW1MNYGER.GER.
I will continue to search for how your Jacob Treffeisen fits in with the larger Treffeisen family of Bickensohl, Germany.