You asked "Are we some kind of cousins?"
That is the 64 Dollar Question, depending on how Benjamin fits into the Peter Hallock tree. My grandmother's Hallock line back to Peter the Puritian immigrant to Long Island in 1640 is:
Inez Hallock-10, Morris Wells Hallock-9, John Kasar Hallock-8, Bethuel-7, Zachariah-6, Zerubabel-5,4, Thomas-3, William-2, Peter-1 Hallock
According to the Hallock Genealogy, Patience Hallock, the mother of Gov Thomas Corwin of KY is:
Patience-6, William-5, Peter-4,3, William-2, Peter-1 Hallock
According to Mary (Conn) Hallack's obituary, she was an aunt of Ohio Gov Thomas Corwin. The only way I am seeing that now is by Benjamin Hallack, her husband, being a brother to Patience Hallock, the governor's mother.. That would make her an aunt by marriage. But, the Hallock Genealogy has already given a brother named Benjamin to Patience who stayed on Long Island. And, how would that fit into the Paxton Genealogy that Thomas Hallack was Benjamin Hallack's father.
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Thanks for the info about Jacoby's death. It sounds like the family had split. Did they get divorced? Or, was the separation due to a job that Jacoby landed in Illinois?
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The Rachel you speak of is the daughter of Jacoby & Lucinda (Dill) Hallack. She was named for her aunt, Jacoby's sister, Rachel Hallack, who married Ezekiel Thurston. He died before 1850 and she was running the Hallack Hotel with her son(s) in 1850 in Paris, Bourbon, KY. She eventually sold the Hallock Hotel in Paris and moved to Cincinnati in 1870 and St Louis in 1880. In 1860, she reported RE=$40,000 and PP = $20,000. In 1870 she showed she was innkeeper with RE=$0 and PP=$10,000 - showing she didn't own this hotel.
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The Phebe Corwin who married Francis Dill was another sister of the Gov Thomas Corwin and daughter of Matthias and Patience (Hallock) Corwin. Do you know how Francis is related to Lucinda? This is probably yet another tie between the governor and the Kentucky Hallacks. I wish all this info would lead to some final conclusion of how Benjamin Hallack is tied into the Peter Hallock tree, but haven't yet found the smoking gun - just all of these coincidences keep popping up.
When somebody as well-known as Gov Thomas Corwin (also later Representative who was a leader in the opposition to the war with Mexico and then appointed by Lincoln to be Ambassador to Mexico.), his papers are donated somewhere. I wonder if in the thousands of pages of papers that might be his own papers might be a mention of his mother's family and who they were - and a tie to Benjamin Hallack, and then a tie into Peter Hallock's tree.