Don’t be concerned about
controlling the horse with the reins. When you are establishing “forward” in the horse, the only rein you usually need is an opening rein. Remember you will be riding circles (page 79, Forward: Riding with Eloise King) for the most part when you start your mounted work or you will be using the arena wall or fence (page 82) as a soft aid. You should not need an outside rein in the initial stages of training or retraining the horse.
Some people say that you need to support the outside shoulder with that outside rein. Losing that outside shoulder generally comes about when you do not have forward established in the horse and/or are over-aiding him. Go back to your basics; forward, check your position, etc., until the horse is strong and supple enough that the outside rein is no longer a blocking aid (which will pop that outside shoulder) and becomes the soft aid that it should be.
If you ever feel that you have lost control of the horse, go back to your circle. Twist your shoulders in the direction you want to turn, use an opening rein to that side and step into the inside stirrup. Stay balanced on top of the horse and relax (especially your legs). Breathe and you will soon be enjoying the ride.
I have only heard of Nuno Oliveira through various other sources and have always been very taken by his training ideas and theory. Not training with force but with feel is something that is an uncommon sight nowadays. Luckily though, we can still see and learn these lessons through people like Sylvia and Eloise, but it is still mostly an uncommon sight even though it was second nature to the great Masters almost half a century ago.
In classical art, one sees horses on loose reins, but with complete collection and self-carriage. The hind quarters are always strong and well-developed. The horses show strong backs. The saddles are placed well back on the horse, often with a crupper. The word that always came to my mind as I looked was “balance.” Horse and rider are in balance.