I would be very confident that this is the right person. You mentioned a daughter named Nellie, and I hadn't looked up any census records. I found the 1900 census for this family (mistranscribed as Vanterpoole) in Manlius, Allegan County, Michigan. As rdpiet pointed out, Dutch naming conventions for children were that the oldest son was named for his paternal grandfather, and the second son for the maternal grandfather. The daughters were named in the reverse - the oldest for the maternal grandmother, and the second for the paternal grandmother.
Fannie Sarah Klaasen shows up as Sarah Klaason in Muscatine, Iowa in the 1860 census, 10 years old and born in New York (matches Fannie van der Zande). Her parents are Martin and Jane Klaason. In 1870, the family is living in Grand Rapids, MI and in 1880 in Holland, MI (wife's name is Janna here).
In the 1900 census, the oldest son is named Andrew (matches Jacob's father in the Netherlands birth record), the oldest daughter is named Jennie (matches Fannie's mother's name), the second son is Martin (matches Fannie's father's name), and the second (surviving) daughter is named Nellie (which, as you pointed out, is very close to Neeltje). This family went very much by the Dutch naming conventions.
I don't have any doubt that you have the correct Jacob Albert van de Zande.