The connection between Robert Cooke Cook and George Augustus Frederick seems to come from Ancestry.com, based on an unsourced pedigree. Obviously, even the ancestry.com source was not listed on the profiles. There's even a GEDCOM file so listing George IV as Robert's father, but I doubt there's any proof to it.
Robert Cook did exist and he married Sophia Kemp in Dallington, Sussex, England and they had 11 children. I've not confirmed their death dates or places or immigration. Nor do I know which Caledonia in what is now Ontario that Robert, Sr. and Jr., both apparently drowned. The profile doesn't list the county.
Was Robert the son of George Cook? I don't know, but I believe his profile needs to detached from his father's. No one offering comments seems to say anything about George IV of Hanover having any illegitimate children.