Ron, I don't have an actual Perlmutter tree-- just a lot of questions.
First, Harris P. didn't marry a Schatz. His daughter Rose married and then divorced Meyer Schatz in New York in the early 1900s. They had a daughter named Maisie/ May Schatz born 1903. All of that is from US Census 1910 and 1920 and from the marriage index at the ItalianGen site.
I don't even know for sure that Harris is the Perlmutter I am related to. All I know is that my mother told me she had an uncle, "Mr. Perlmutter," who was an auctioneer on Lispenard Street. And that he "had a son named Sam who was a pawnbroker and had no children." The only people I've been able to find who fit those descriptions are Harris P. who was an auctioneer with a business on Lispenard St. from about 1915 to 1920+ and a Sam who lived in Spring Valley, NY in 1910 and in Perth Amboy, NJ in 1920 and was a pawnbroker/ loan broker. He had a wife named Pauline and no children.
I have not found any link between the two. Harris arrived in NY in abt. 1889 from "Russia" and was married to Fanny for 31 years as of 1900 census, but she was his second wife. There is no Sam in the h/h in 1900, but the Sam I found was old enough to have left home by then.
My mother was born in 1902 in Manhattan, later living in the Bronx. Her father was Sam Feinberg (originally Daiboch) and her mother Jean Frances (Fannie) Vilner. Fannie's father died when she was three years old and Vilner was her stepfather's name. On her death certificate, her natural father's name is given as Abraham Petruskitz.
I don't know on which side "Mr. Perlmutter" was related, nor do I know whether he was an uncle by marriage to a sister of one of my grandparents. I don't know if the first wife may have been the actual relative and son Sam from the first marriage.
I do know that my grandparents lived in Wisoke-Litovsk, Russia/Poland, now Vysokoye, Belarus until 1900, not in Ukraine. And I know they were Litvaks. This doesn't rule out Ukrainian connections and I think there were some.
Other names my mother said were related were: Rosenman, Sobel, Gellis. Do any of those turn up in your family?
I'm afraid that's all I know so far.
Joy