This is an image of the 1870 census of the Mulvan(e)y family. James gives his age as 42 - he's only aged 8 years in the past 10, but with this age, his birthdate would be around 1828. Bridget has aged 10 years in the past 10 years, from 28 to 38, so her birthdate would remain the same, around 1832. James is listed as a Carpenter, still, and his oldest son Thomas is an "Ap. Carpenter" - he's apprenticed, I'd assume, to learn his father's trade. Thomas, John, and Patrick, at ages 15, 13, and 11, have each aged a neat 10 years in the past 10 years, so their birthdates remain around 1855, 1857, and 1859, respectively. They're joined by younger siblings Mary, 9, (b. 1861?) and James, 6, (b. 1864?). Patrick and Mary are at school. Thomas, as we said, is learning to be a carpenter, John has a question mark next to "occupation" (would 13 be too old for school and too young to work in 1870? I didn't think there was such a thing!), and James Jr. seems not to have started yet. Bridget is listed as a dressmaker in this census. Interestingly, James Sr. has an affirmative mark under "Male citizen of U.S. of 21 years of age and upward." We know James was not born a citizen, but he has become one since arriving in the U.S. Either he went through the entire naturalization process, but Bridget did not, or he could have petitioned for naturalization after service in the Army. According to Wikipedia, "An 1862 law allowed honorably discharged Army veterans of any war to petition for naturalization, without having filed a declaration of intent, after only one year of residence in the United States." It doesn't strike me as particularly likely that he served much time, if any, in the Army during the Civil War, however, due to the timing of the births of his youngest children. If he were away at war from 1861-1865, it is highly unlikely that he could have fathered children born in 1861 and 1864. It's not impossibly, however, to imagine that he may have been away for 2-3 years in between their births.
Betty and John have told me that these names seem to match up with the names they know of of Patrick's siblings, and that they're pretty sure that Patrick's brother John was a Brooklyn alderman.
It seems that the family has moved since the last census was taken. They no longer live in the same apartment building as the John Mulvany family, and are now in a single-family house. There is no record of the value of their estate this year, but it wouldn't surprise me if they were doing better than they had been in 1860, simply because the move from an apartment to single-family house tends to be a move up.
Another record of the family that I MAY have found is in the Baptismal Record of St. Paul's Church in Brooklyn. Mary Ann Mulvaney (spelled with the "e" now) was born April 7, 1852, and baptized at the church April 25, 1852. Parents are listed as James Mulvaney and Bridget Rothwell, and godparents are John Mulvaney and Brid Kavanah. This Mary Ann Mulvaney would be about 10 years older than the Mary Mulvaney listed on the census, and would be about 3 years older than Thomas, who appeared to be the oldest child. The parents' names are correct, as, it would seem that the godfather, is as well, although it's cutting it close for John Mulvaney to be in the US in April of 1852, when it would seem that his son Michael was born in Ireland in 1853 - late 1852, I'd think, at the earliest. Possibly, of course, Michael's age is a year or two off. It seems likely, but not definite, that this is another, older child, a girl who possibly died young, born to James and Bridget Mulvaney before their oldest son Thomas. Is anyone familiar with St. Paul's Church and whether the family were parishioners?