(The app randomly posts without me wanting it)
*the poles will be on the circumference of the circle and you in the middle. Let him pass over the poles and if he touches any one of them you keep him in the circle and have him repeat them. Do this until he doesn't touch any, once that happens you stop him, bring him to you and show him your appreciation. Then repeat the whole process. Soon he will learn to pay attention to the grounds.
This and the transitions should help a lot.
I have seen this a lot in ex- trotters.
Stumbling is usually caused by too much weight being on the forehand. And once overloaded it's easy to stumble. Continuous downward transitions will shift his weight back.
A great excercise from the ground with poles is that you place 2-4 poles, stand in the middle of a circle
Most of the time, it means there's a lake of impulsion or balance. To work the balance, as Kareen said, you can work on ground pole and transitions. About the impulsion, you have to ask him with your legs, he has to be more concentrated and don't let his legs falling :p