I had great difficult trotting round corners - and for many years.
Even out hacking. There are a few things to consider - from both horse and rider.
First you are on a four legged animal and he has to get those four legs and a long body round a "corner". Sometimes we do ask our horses to turnj a sharp right angle but we usually do it by rotating the front legs round the hind legs which stay almost still. The corner of the school as you ride round the outside of the school is more like the arc of a circle. And it may help you go round it if you think of it like that.
Even going round the arc of a circle can be complicated for a horse. Our RI told us to picture 2 railway lines going round the corner. The outside railway line is of longer length than the inside one. The outside legs of the horse need to travel further when going round a corner than the inside ones.
So think of those school corners as part of a circle. You will need to picture the front of your horse leaving the outside track a little way before the corner and then retuerning to the outside track some way after it. I have a great DVD on dressage by Davison and from this I learned that when you picture the curve, you should make those two points equal. And that the longer the curve is, the easier it is for the horse.
So much for the horse - Then there is the rider. We are taught to touch the rein to turn the horse. And it is true that where you put the nose of the horse, the body will usually follow. But I reckon that without meaning to the thing most likely to stop the horse as it goes round the corner is our tightening one or both hands on the reins. You are far les likely to do this if you think of that arc of the circle. It takes more energy for te horse to move on a circle than on a straight line so yes, you do need to create the energy - but try to do that in advance, before you get to the corner.
As a student you will be told to ride close into the corners (and use your inside leg to keep the horse out ) but I wouldnt try that till you can trot easilly round corners, more a question of allowing the horse to do it easilly for himself, possibly on quite a long loop. Once you are going easilly and your horse is happy too, you can add the refinements.