Should I remove, or work around dividing basement walls?
You might as well just remove the stud and small section of plate that contacts the wall. this will allow you to completely insulate the wall and the stud can be re-installed outside the insulation and screwed into the upper and lower plates if you cut them correctly. This will also come in handy when you go to put walls against the insulated concrete. The existing stud will be here you can corner to it with extra sheathing studs and make a proper corner. Canadian codes are very strict, so do it right the first time.