Citizenship Act
Persons who are citizens
3. (1) Subject to this Act, a person is a citizen if
(a) the person was born in Canada after February 14, 1977;
....
(2) Paragraph (1)(a) does not apply to a person if, at the time of his birth, neither of his parents was a citizen or lawfully admitted to Canada for permanent residence and either of his parents was
(a) a diplomatic or consular officer or other representative or employee in Canada of a foreign government;
(b) an employee in the service of a person referred to in paragraph (a); or
(c) an officer or employee in Canada of a specialized agency of the United Nations or an officer or employee in Canada of any other international organization to whom there are granted, by or under any Act of Parliament, diplomatic privileges and immunities certified by the Minister of Foreign Affairs to be equivalent to those granted to a person or persons referred to in paragraph (a).
It comes down to whether a visiting force as that employing your father was is considered to fall under (a) and/ or (c) with emphasis on the granting of diplomatic privileges and immunities. The Visiting Forces Act ties closely to the NATO Agreement regarding the status of Forces (the VFA almost lifts word for word clauses from the NATO version) including limitations on Canada's law enforcement and judicial systems on prosecuting for crimes, waiver of duties and taxes, exemption from immigration formalities (hence your mother's unrestricted entry).
If it looks like a duck, walks like a duck etc. My take is that Visiting Forces have diplomatic status and/or conditions similar thereto. The only conclusive response would be from the Protocol Office and I don't see them rushing out a response in your favor. You can trawl through Federal Court case law too. I do recall case law on someone born in Ottawa who got a Canadian Passport and 20 years later their renewal application was bounced as CIC found his father was a consular officer so Passport Canada can revoke when the situation is clarified or comes to their attention.
Apply you have nothing to lose.