I'm glad to hear from you. My gggg-grandmother was Mary (Hopkins/Appleby) Van Horn, who was William Ivins Appleby's half-sister. Their mother was Mary (Luker) Appleby, but my ggggg-grandfather on this line was Mary's first husband, John Hopkins.
Do you have the genealogies of both of Wm. I. Appleby's parents, or just the Appleby line? I have seen undocumented sources that say Mary (Luker) Appleby was the daughter of Thomas and Amy Luker, but have never found proof of this relationship. Her Luker surname and Monmouth Co, NJ residence suggest that she was a descendant of Thomas Luker, the apparent namesake of the town of Toms River, NJ.