Using some info from your posting history, here's my best guess for Michael's family in Bridgeport::
I searched the 1900 Census and about the only match was Mary Urbanowski a widow, from Austria who immigrated in 1897.The family is living in Bridgeport, Ct. and her son Michael was born Feb 1884.There's also 3 other children, Helen 13, Edward 9, and Rosie 2 (she's born in Ct.).
I found this family atthe Castlegarden.org site with the surname Urbanowska,(Ellis Island also has them listed on their site) with arrival date of Nov 28, 1896.
Checked Ancestry.com's Bridgeport City Directories, and Mary Urbanowski is listed in all the available directories until 1925 as, Mary J. Urbanowski, widow of Joseph.Michael is listed as living with Mary in the 1904 and 1905 directories.Michael is not in the 1907 book, which may mean he moved (which fits with him moving to NY??).
I couldn't find Michael in the 1910 census, but did find Mary in The 1920 Bridgeport, Ct Census.She's age 62, and living with her daughter and son in law, Frank and Rosalie (Rosie from 1900 census) Jawoisz.This could be the daughter she attended Michael's funeral with.
I see that Michael's first born son in the 1920 census, was Joseph (after his father?), and thou the writing is hard to read, it looks like Mary's name was Marie when she immigrated on the passenger list,and Marie was Michael's first born daughter's name.
This family seems to be a pretty good fit with the limited amount of info that you have.