I thought I could canter around the ring?

I always knew that just when you think you know how to do something on one horse, you get on another and he really tests you. Chance is that horse, because he's green and he does EXACTLY what I ask, meaning all those cues I don't realize I'm giving, he picks up on. So I'm not yet able to canter around the ring on him, because we go down the long side and once we get to the corner he falls in and we find ourselves spiraling into a tighter and tighter circle. It feels like we're going to topple over! As my instructor pointed out at the end (too late to correct that day), I need to put weight in my outside stirrup, while keeping leg on inside and...okay I don't remember what I'm supposed to do with my reins? Open the outside rein? Open the inside rein? Cantering has gotten so much more complicated! The old lesson horses just stay on the track and go!