Your family appears to be in Slatington P.O., Coplay, Lehigh County, Pennsylvania, in 1870. I can't find them on familysearch or I would post a link. The oldest son in the family is Manus Matthew, born 1864, Coplay, PA, according to his death record. Others in the family are:
John, born c 1866
Hugh J, born c 1872
James, born c 1874
Mary, born c 1879
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Also in Slatington P.O., Coplay, PA in 1870, is this family:
Michael Sweeney, 35.
Ann, 30
Catherine, 9, born in NJ
Mary J, 7, PA
Manus, 4
Annie, 2
John, 1 month
So Michael also has a son, firstborn, named Manus. Manus's death record said that his mother was Ann McCue. Second son in both families is named John.
This is probably not a coincidence. Maybe brothers married sisters. So you have 2 Sweeneys and McCues to look for. And the father of your William and Michael could be named Manus or John. The McCue father would be the other name.
Since Michael and Ann's daughter Catherine was born in New Jersey, that is probably where they are hiding in 1860. You might find them all with their parents.