I am a Canadian-South African dual citizen. My daughter is going to pursue a Master's degree in the US. But since it's her first trip abroad, I want to accompany her for the 2 years duration of the course or at least the 1st year. Since I am a Canadian, I can travel to the US visa free for 6 months, and since I am a South African too, I can apply for a 6 month tourist visa as well. Is it allowed that I use this to accompany her for at least the whole first year of the course by travelling to the US first as a South African citizen and then visa-free as a Canadian citizen?
You can stay in the US for as long as the immigration officer at entry admits you for. You can leave the US and seek to re-enter the US as soon as you want. So, for example, if you were admitted for 6 months as a B2 visitor the first time, you can leave the US, immediately turn around and seek to re-enter, and, if the immigration officer decides to admit you as a B2 visitor for another 6 months, you can stay for another 6 months, and you can potentially do that again in another 6 months. There is no technical rule that the officer cannot do that.
However, if you have stayed for too long too many times recently, there is an increasing chance that the officer will deny you entry as a visitor for failure to overcome the presumption of immigrant intent. For the purposes of that determination, there is no reason why the officer would do it differently based on if you are presenting a Canadian passport or a South African passport, if the officer finds out that you are the same person. If the officer asks about your recent trips to the US, you must answer honestly regardless of which passport you used to travel to the US the last time.