I agree with WB. YOu are advancing the inside shoulder too much. This will cause your horse to mirrow you and advance his inside shoulder too much, stay a bit bent to the outside and his hips fall to the inside of the circle. AND you are gripping up with your outside lower leg. Can see it well in the first part of the video.
So, you need to canter and think about your shoulders being alinged withhis (or at the angle his shoulder SHOULD be) If he is on a circle, and you draw radius lines out from the cirle, one for his hips and one for his shoulders, which are slightly in front of the hips, of course. Those radii are what you need to align your hips and shoulders with; your hips line up with the horse's hips and the radius that they are on, while your shoulders line up with the horse's shoulders and the radius that is is on. So, if you are circling left, as you were in that video, your shoulders will have what feels like a greater turn toward the inside of the circle than your hips do, because they are on a different radius line.
You may advance the inside shoulder only momentarily, with the landing of the leading leg, and then draw your shoulder back into it's place during the next phase of the canter; the moment of suspension and the next two phases until once again, the leading leg hits , the horses inside shoulder is momentarily advacned and you , too , can advacne your inside shoulder a wee bit.
but you are sitting overall twisted with your upper body too far inside and you are also leaning a bit too much into the circle (like a motorcylce rider leans into a circle)
As for him having his hips drift to the inside, I can totally see that. Rather than trying to shove his hips back to the wall, move his shoulders over so that they track in front of his hind.. create more inside bend and use a bit of outside thigh and outside rein to encourage him to move his shoulders to the insdie of the track. He will come off the rail more, but be better aligned and it doesn't matter where he goes as long as he's moving straightly.
You will want to relax more, if you can, and look up and let him carry you for a bit. I always think we work too hard at the canter and end up interfereing with the horse. I know I do. I need to remind myself to relax and let him do his job. He's been cantering for years! He knows how to do it.