Hi Lynette,
It's Norm's youngest son Leigh. I was doing a bit of research online and also got to about the same place as you.
Couldn't find any trace of Dominick in births and deaths in England or Ireland. I did find an entry in the 1861 census for Bridget Birk and all her kids (including James Burke, at the right age for that year) at the right address in Coventry. Interestingly, Bridget and her eldest son are listed as Birks, and the rest of the children are listed as Burkes. She was listed as a widower, so Peter Burke must have passed away between their marriage in 1838 and 1861.
In the 1871 census Bridget Birk and Bridget Burke had disappeared. I was able to trace through one of the kids and find that she had remarried a Patrick Caulfield, was still living in Coventry and had 3 of the kids still with her.
Most of the sons seem to be listed as watch makers in most of the earlier censuses. Later I traced one of the sons until he became a cycle maker (bikes maybe?).
I also found some good census information on Lucy Dyke who married James Burke and emigrated to Australia. Another interesting note is her father Thomas Dyke was also in the watch industry as a watch maker, although I think Coventry was known as a watch making area.
I have screenshots and photo versions of census info if you're interested