To start with Mordechai Szwarc. We know he was born in Brzeziny probably in 1777(?) and died in Zgierz for sure in 1843. He was married to Hana daughter of Moshe who was probably the mother of the three surviving (at his death) children:
1) Abram 1816-1855 born in Brzeziny, lived in Strykow, married Esther Abram, had at least one son named Jacob and is probably the ancestor of the newly discovered relative in the US (I finally figured out that the word after Abram in Mordechai's death certificate is "cyrulnik" - referring to his occupation "barber-surgeon"). .
2) Hersz Ber 1818-1887, born in Brzeziny, married in 1844 in Brzeziny to Haja with whom he had a) Mordtka born in 1844 in Zgierz and – probably – b)Juda Ber born in Brzeziny in 1856, c)Majer Ber who married Fryma Sztotland in Brzeziny in 1873 to whom was born Wolf Lajb in 1878 in Brzeziny who married Felicia Kino and had Fredek, Eva, Bela and Ela (the mother of Jean Dumas) d) – for sure – Hana 1857-59 born and died in Zgierz. In 1859, Hersz Ber married again (marriage record not found, probably in Zgierz) to Miriam Gliksman 1843-1887. Their only son e)Issuchar (Sucher Moshe) was born in Zgierz in 1859 and died in 1939. He married Sura (Salomea) Gliksman (1861-1837) in 1879 and they had the 10 children that we know.
3) Kiwe (Jaakov) 1822-1866 born in Brzeziny, died in Zgierz. Married Gitla Gutkind. They had a son, Israel, born in Zgierz in 1855 who married a Golda and died in Warsaw in 1937. Israel and Golda had a son. Maier, born in Zgierz in 1879 who married Regina Prager born in Zarki in 1886. Their son, Michael was born in Bedzin in 1909 and married Marysia Frenkel and they had Rafi, Meira, and Rina.
We are not at all sure of the names of Mordechai’s father and grandfather. The idea that they were called Hersz and Alexander is speculative. There is no proof. The names Abram and Jaakov are equally probable.
With respect to the Gliksman side Wolf Gliksman 1825?? (Radomsko???) -1880 marries Zysl Tenenbaum 1832(in Checiny)-1898. Mariem Rajzal is born in Radomsko in 1851 (she is probably the Malka Gliksman who marries Izrael Boruch Glicensztein in 1872 in Zgierz and gives birth to the painter, Henri Glicensztein). Jakob is born in Radomsko in either 1859 or 1860. [There is another Mariem Gliksman born in Radomsko in 1861]. Salomea (Sura) was born in 1861 in Zgierz. Then Mosze b 1966 Shmuel b 1869 Zysa Bajla 1872 all in Zgierz.
Jakob Gliksman had 12 children. The youngest Sophia must be born after 1900. Jacov maried a Zippora Stupaj who had at least two other sisters Mania in Wroclaw and Gucia the mother of Adam Waks.
(Because there are a lot of Shmuels in the various families I think Wolf’s father might have been Shmuel but Jacob is another good possibility).