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I have stayed up to place this, Carl married my great Aunt Emily Bowler from Penarth South Wales UK. He was born in Nova Scotia c1903 died 3 March 1979 Victoria British Columbia, confirmed by the local library in Canada. Would love to find any siblings, parents, "anything" at all about the Parker family in Canada, sorry really need to sleep ! will check in morning oh it is lol will check when I get up lol

TWG
in South Wales UK very very tired and in pain lol

There is a Carl Parker, born Nova Scotia, c1902 (the dates are incorrect for a lot of my rellies, so don't trust the year that is written for Carl). You can view the actual image.
http://automatedgenealogy.com/
In case you can't read it, it looks like they were living in Port Greville.

It looks like two of Ross' sons were seamen.

There is a Carl Leslie Parker marrying Regena Dorothy Willigar in 1928, Cumberland County.
https://www.novascotiagenealogy.com/
It also shows the marriage for Ross and Lillian and a death for a Ross Parker in Shelburne, Shelburne County in 1913.
A possible death for Lillian in Parrsboro Chapel, Cumberland County, 1941. (Edgar Parker, from the 1911 census, shipped out of Parsboro, NS in 1930.)

You may be able to get a copy of Carl's death certificate which MAY include his parents' names. All of my Canadian death certificates do include parents' names and some include parents' places of birth, however, all of my records are from the early 1900's.
http://www.bcarchives.bc.ca/BC_Our_Collections/BC_Vital_Rrd_Collect.aspx

There was a Regina D. Willigar, born 1911, died 1949, Parrsboro, Cumberland, Nova Scotia.
http://24.215.88.44/Alldata/dat2130.htm#1
If that doesn't work:
google: "willigar, regina"

Photograph of her headstone:
http://24.215.88.44/graves/NS/Cumberland/NS%20Cumberland,
%20Parrsboro%20(St%20Brigid%20Cemetery)/index2.html (I added a line return between Cumberland, and %20 so it would fit on this page.)

The Willigar family is also on AutomatedGenealogy. (Father was Walter, mother was Mary.)