I can't say whether Frederick John was or was not related, he is just the only other Broderick that died in the very same locality as a couple who MAY have been his parents. I have no access to the 1891 census (5 years before Frederick died) but it may be him I found working with a photographer in 1881. Perhaps the Hove cemetery has a burial record of Frederick, Denis and Catherine? If they share a headstone or were buried together, that would suggest a family tie.
Also, as stated before, to find out what wealth they had and perhaps where it came from, wills (English or Irish) would seem to be a good source of info as would obituaries. But to ease the search for the latter, you would still need a more precise day and month of death. Hence the need to contact the cemetery or alternatively, to purchase a death certificate. Otherwise, alowing for 2 weeks either side of the death quarter, you will just have to plough through the columns of anything up to 4 months worth of local newspapers, just on the off chance of finding something.
Roy G