What your instructor is asking is that you keep the outside rein steady and supportive but still following the horse's mouth, and with the inside you are "asking" the horse to give to the bit. She might ask you to kind of "tickle" the horse's mouth with the inside rein, no? It shouldn'et be like a "see-sawing" motiion, but you want to get the horse's attention and suggest that he/she stop bracing against the reins and put a litltle softness into his poll, bending a bit. The minute that horse gives to the inside rein, even the tiniest bit, you stop asking with the inside rein and do NOTHING for a sec. This says, "yes, that's what I wanted you to do". Of course, the horse will raise his head up again, you do a soft vibration of the inside rein and pay attention for his GIVE so that you can reward it pronto. Do it over and over and soon it will take less and less to get the bend. The reason you don't use both reins is that it can give the horse something to fight /brace against. Most horses feel trapped if the reins are on them at equal pressure. You should talk to your horse with one rein more than the other, always.
As for whether that horse will be hot when it hasn't been ridden much lately, is it in all day turn out? That will make a huge diffeence. Is it being fed grain? Try leading it around a bit. You can get a really good feel of a horse by how he leades. The horse at the end of your leadline is the horse that will be at the end of your reinline, no difference.
If there was a round pen, I would work with him there as you can also get a really good feel for his attitude.
I am not a young person, so I need to be more careful, as I