Hi. I am an IrelandXO volunteer living in Limerick but not originally from here so I am at a slight disadvantage when it comes to putting you in touch with the people you want but I can ask some people who grew up here. I can remember the pharmacy on the Ennis Road not far from Sarsfield Bridge because I lived near there when I was a student here back in the early 1970's. It seems to have been called the Belfield Pharmacy. According to the obits for the the family names you identified above in the Irish Independent they lived at 50 O'Dwyer Villas, Thomondgate, less than a mile from the pharmacy. I also see that the info about the will administration papers appeared in the newspapers.
I found a death cert for Robert Mulrooney, a "Chemist's Son" who drowned at 11 years of age while swimming in Kilkee, County Clare in 1937. I think this will be their first son because his name coincides with the name of his grandfather and he would have been born the year after they married.
I found some information about Patrick's family. His parents Robert Mulrooney married Mary-Agnes Francis who married in St Michael's Church on Apr 28, 1897. At that time he was working as a clerk living in Limerick. His father Patrick was an Ex RIC officer and Mary-Agnes's father Anthony was a sailor. Robert appears to have become a travelling sales rep some time later and took up residence in Tipperary Town. Children found:
20-Mar-1878 Patrick Joseph, Born in Tipperary
12-Feb-1900 Mary Catherine, Born in Tipperary
15-Feb-1902 Elizabeth, Born in Tipperary
26-Jan-1906 Agnes-Ita, Born in Limerick
The family was living in Kilrush, County Clare when Patrick married Mary Quinlivan in 1925. His grandmother Catherie Francis was born in Clare according to the 1901 census so this might have had something to do with it.
Not sure how much of this you already know or which one of the family connects to you. I can try to find out some more but in the case of living people I can't publish any details here.
Tim O'Connell (darragh@IrelandXO.com)