I am not a Gulick Family student, but given the paucity of primary records the best evidence of the Rensche's mother's name and family lies in the apparent fact that she named one of her sons Minne.
This indicates that the child Minne^4 Gulick is named for his Uncle Minne^3 Van Sicklen and ultimately for his great grandfather Minne Johannes, in the Dutch fashion.Minnes Johannes' wife, and the mother of the only wife of Ferdinandus^2 of whom I have ever found indication, Gertruy Minnes Johannes, was Rensie Feddans--the namesake, no doubt of Rensche^3 Van Sicklen herself.
In his will, Ferdinandus^2 mentions his wife Gertruy, sons Ferdinandus and Minne, and six daughters, Eve, Renige, Elizabeth, Mary, Annie and Janette [NYC Wills. Liber 15:199].The boys are named in birth order and one assumes the daughters are as well.This, too, indicates that the grandmothers were Eva Jansen and Rensie Feddans.
The only caveat to this would be if you know that Minne Johannes and Rensie Feddans are also ancestors of Johannes Gulick and/or the nephew Gulick. Or. was there a Minne^3 Gulick?
I would be interested in learning who the others wives of Ferdinandus^2 were, according to the source you mention.