Thank you for writing.
Yes, you have the right family. I don't have a lot of information - she was only 36 years old at the time of her death. The others in the grave (called cemetery) are her single children and husband. As far as I know, she had at least 8 children (women listed with married names):
Mary McCann 1866-1894
Anastasia Russlend 1876-1958
Margaret Van Name 1881-1913
If her year of birth from the DC is correct, she was born in 1847-ish. That would make her 17 at the time of John's birth. Her DC says her mother was born in the US and father in Ireland.
Her obit didn't list a Church for funeral services. It was a small obit that just stated her married name (but with the middle initial C - not sure what it stands for), date of death, age, her husband's name and her address.
The married couple lived in Vinegar Hill section of Brooklyn. I have her listed in the 1870, 1875, 1880 NY/Federal Censuses.
I just noticed an hour ago that familysearch.org added an index of the 1855 NY census (yay!) but a search of Margaret Tompkins/Thompkins didn't have any hits that I think make sense.
I tried to flip thru the un-indexed 1865 NY State Census but haven't found them yet.
Hope I haven't babbled on too long.
Thank you again,