At first glance it appears that Maria Schoonmaker, who m. William Jacocks, and who is said to have had a brother, William Henry Schoonmaker; might be the Mary Jaycox, who had a brother,William Henry Schoomaker, and was the 2nd wife of Capt. Hoysted Hacker. There is, however, a date discrepancy. You have Mary Jaycox as b. ca. 1745. William Jacocks d. 1817. At least one sibling of William's was b. 1783. It seems, then, that Maria and Mary are the same person. I think it very likely that they were related; perhaps closely. However, if Mary's brother was a William Henry Schoomaker; then one might assume her maiden name was the same as his. This suggests that Mary was a widow when she m. Hoysted. The Jaycocks, by this period, had been in North America for 150-200 years, and had grown to a very large family. The complication of the spelling of their surname, plus their propensity for using the same forenames, makes it difficult to trace them with accuracy without doing actual research in New York archives and libraries. I suspect that much the same could be said of the Schoonmaker's/Schoomaker's. I would be relatively certain, from time and location and the coincidence of similar names, that Mary Jaycox was related to the overall Jaycocks' family; if only by marriage; but I would be at a loss as to say how she was connected. An example of the spelling difficulties is:
BENJAMIN DESOBRY JACOCKS
His middle name likely represents a connection to the Disborough, Disbrow, Disboro family. As to the spelling of his surname; could be anything from Giccoc to Jaycox. My own connection comes from the earliest days of the family, and attempting to trace further generations has not been an effort I have been willing to make; aside from the weak attempt to rationalize scattered notes in the posting to which you refer. In short, trying to sort out the Jaycocks scares the willies out of me! Also, I feel the Jaycocks (connected or disconnected) are your relatives, as well as mine, but I cannot envy you the task of defining that relationship.