According to the Description Book of the 2nd Battalion of the 14th Regiment of Foot referred to above in Ancestry's Canada, British Regimental Registers of Service, 1756-1900, Isaac Pickstock has a date of birth of 8 June 1790. If true, this means he cannot be a son of Richard Pickstock as Richard and his wife Margaret / Peggy nee Woodward, have a daughter, Nancy, born 7 April 1790.
However, I have just realised that the Description Book's dates of birth on these pages are nonsense. When comparing the column headed "Date of Birth" with the column for date "Enlisted in the present Corps", it becomes clear that the day and month for the birth are identical to the day and month that the soldier enlisted.
Looking at the page for Isaac, 8 soldiers have a "Date of Birth" completed - all joined up younger than 18 and all have an enlistment day and month equal to the birth day and month. Assuming that the Army would accurately record the enlistment date, the only possible explanation is that the birth date is a purely nominal value based on the age at recruitment, and that Isaac could, therefore, have been born any time in the 12 months prior to 8 June 1790 - if the age is even correct.
I did wonder if Isaac might have been a twin for Nancy, but Nancy is recorded as baptised at Witton (i.e. Northwich), Cheshire, and there is no sign of a twin brother for her.
So - the major objection to Isaac being Richard's son seems to have fallen by the wayside. Though it's still not clear where he might fit, other than possibly between Nancy and her parents' marriage.