Each Province's Wildlife Act specifies the resident qualifications for their jurisdiction (Province). Typically there is a time period of physically residing in the Province. In the interest of ending any "street lawyer" debate quickly - I will quote directly from the Acts and Regulations of each jurisdiction.
Ontario's Fish and Wildlife Conservation Act defines resident (in S. 1 definitions) as:
“resident” means a person whose primary residence is Ontario and who has actually resided in Ontario for a period of at least six months during the 12 months preceding the day that residence becomes material under this Act, and includes a person who belongs to a class of persons deemed to be residents by the regulations;
Regulation 665/98 (made pursuant to the Act) further specifies:
3. The following persons shall be deemed to be residents for the purposes of this Regulation and Ontario Regulation 670/98 (Open Seasons — Wildlife):
1. A person with diplomatic credentials in an embassy, consulate or trade commission of a foreign government who has taken a post in and resides in Ontario.
2. A civilian employee of a service agency attached to the staff of an embassy, consulate or trade commission of a foreign government who has taken a post in and resides in Ontario.
3. A member of the armed forces of a foreign government who is stationed in and resides in Ontario.
4. A member of the RCMP or armed forces of Canada who is stationed in and resides in Ontario for at least one month.
5. A civilian employee of the RCMP or armed forces of Canada who is stationed in and resides in Ontario for at least one month.
6. A member of the armed forces of Canada whose primary residence is Ontario and is temporarily posted outside of Ontario.
7. A member of the immediate family of persons set out in the paragraphs above who lives with the person in Ontario. O. Reg. 665/98, s. 3; O. Reg. 49/11, s. 1.
So you see in Ontario - physically living in the territory is essential to having resident status. In Quebec, it is very similar - the Act (An Act Respecting the Conservation and Development of Wildlife, RSQ, c C-61.1) - Section 1 "definitions" states:
“resident” means any person domiciled in Québec and having resided there for at least 183 days during the year preceding his fishing, hunting or trapping activities or his application for a licence or a certificate;
So the answer (which you suspected) is NO. You cannot hold resident status in both places. You also cannot arbitrarily choose which one you want to be a resident in. When it comes time to buy your licences, whichever place you have been living in (continuously) for the past 6 months before that day is your resident Province.
Hope this settles it for you.