Thanks to Mr. Willem Huycken, I've come across a branch that involves about five families that are unconnected, mal-connected, somewhat conflated and have a few duplicates.
Based on various sources, I've built a basic outline of how the families involved should apparently look: https://www.wikitree.com/wiki/Space:Quackenbush-118_Sandbox
It seems the best way to collaborate here would be to take it bit by bit.
Firstly, it appears that the de Haerdts and the van der Hards have been conglomerated into one family.
The van der Hard family
This family was from Nieuwkoop, Zuid-Holland. Aart Sijmonsz and Geertgen Stoffels had at least three children: OpenArch
Their son Sijmon and their daughter Lijsbeth were both settlers. The baptisms for both have been located but the indexes say the images are at GaHetNa, and GaHetNa says that the Nieuwkoop en Noorden book is not online.
The de Haerdt family
This family was from Buren, Gelderland. In some cases, it will take some digging to find the record that states as much for each, but Jacobus gave Buren as his origin at his wedding. Balthazar named his siblings in his will; Daniel, Matthias, Jacobus and Willemtje. Those same people, or people closely related to them, can be found as witnesses at the baptisms of Jacobus' children. Balthazar, Daniel, Matthias, and Jacobus were all settlers. It doesn't appear that Willemtje emigrated but her son Daniel eventually did.
In the NJGBS file for DeHart, Jacobus' parents are given as Willem de Hart and Catalyntje Daniels, but the source for that is not given.
The other weird thing about this conglomerate family is that the children of the families above repeat for a few generations; as the children of Symon, Aart's father https://www.wikitree.com/wiki/DeHart-357 and as the children of William, that Symon's father https://www.wikitree.com/wiki/DeHart-152 So those all might be duplicates as well.
No clue who Dorite de Hart is supposed to be. Perhaps that is the Dirck that the van der Hards baptized in 1649?
Once we get the two families sorted, perhaps we can look at their duplicates.