I think you are very close there. It does seem almost irrefutable that there is a relationship between William Jaycocks and the Widow Hacker; and, as you say, most likely a sibling relationship. The question I would ask is, "Was Capt Hoysted Hacker still living in 1817?" If not, then I would accept that his 2nd wife was likely William's sister.
Accepting that, I would also accept, with very little room for doubt, the William (and therefore Mary) were members of the Jaycocks family as found in Hempstead, Long Island, NY in 1698; and so on back to Francis and Grace.
Another assumption, which I have already made or accepted, is that William Jaycocks (therefore Mary) was the s/o Thomas and Jemima (Sherwood) Jacocks. I note that Thomas b. ca. 1762, d. 15JUL1817, apparently also left a will in 1817; but do not know if I have seen it or an abstract. It may be worth hunting down.
On the other end of things, I am pretty sure that this part of the family is descended from Francis and Grace's son, William Jaycocks bpt. 12AUG1627, still living in 1670. So far as I know, the three sons of William were:
J1. DAVID JAYCOCKS m. HANNAH _____
J2. JONATHAN JAYCOCKS
J3. BENJAMIN JAYCOCKS under 21 in 1694, in Fishkill 1737-1740, m. 1JUL1741 JANETTJE JONES
One of these may be the grandfather (or father) of Thomas (ca. 1762-1817.) For what reason I do not know, but I seem to have suspected Benjamin as a father. It is at this point that I find I simply have not enough information. The key may be to concentrate on the family in Poughkeepsie. All-in-all, I think you may be very close to establishing a line-of-descent.
Another possibility, just to confuse things, was the s/o FRANCIS JACOCKS m. CAECILIA (SUSSELE and variations; Cecelia?)_____. (Francis possibly son of David [J1] and Hannah Jaycocks of Hempstead, Long Island in 1698.) This son, also Francis:
J133. FRANCIS JACOCKS Queens Co., LI b. ca. 1737, (in 1790 census of Poughkeepsie?), m. Dutchess Co., NY 27JAN1756 MARITIE (MARITJE, MARY) WILTSIE (b. Queens Co., Long Island, NY 22MAR1739), daughter of Hendrick Teuniszen (Theunisen) and Pieternelle (Van de Boog) Wiltsie of Jamaica and Dutchess Co. (Francis and Maritie had 15 children)
had (amongst others) two children:
J1335. THOMAS JACOCKS b. 1762, bpt. 12MAY1762 Zion Lutheran Ch., Loonenburg (Athens), Greene Co., NY
J1337. MARIA JACOCKS b. 1766, bpt. 6JUL1766 Poughkeepsie Dutch Ch., m. 1JAN1785 HENRY (HENDRICUS) I. WILTSIE (b. 5SEP1765, d. 5DEC1838), s/o Isaac and Catherine (Swarthout) Wiltsie
What is interesting here is that the earlier children are given as baptized in Greene Co., but that Maria was bpt. Poughkeepsie; suggesting a return to that area. Again, if this Thomas was the father of William and, presumably, Mary, I cannot say.