The 1870 census showing Denis, Patrick, Alexander and the father James was of Pittsburgh. It's still possible it is the right family, but not if the right family was from Philadelphia. Considering the same undertaker was used for the father Dennis as was used for Patrick makes me feel there is a connection. Also they're buried in the same cemetery. Follow through with contacting the archdiocese archives in Philly. The church they were members of probably buried everyone in the family and perhaps even married a few of them as well. You might also try the cemetery office. I'll bet they're buried together.
The 1880 census of the family I found is Killen, but the K sort of looks like an H. I say it's a K, someone else might read it as an H. However, the names and ages basically match the names and ages of the 1870 census of the family Killon.
Brother Dennis may have gotten older brother Patrick involved in fighting.