Don't be hard on yourself! Ok, so you may feel a bit disappointed that you weren't as cool as a cucumber the whole time...but playing buffer to a wizzy pony isn't something that happens on every lesson, in my humble opinion, that is more something that people learn to do when they have their own horses or work on a yard where there are young/nervy horses being brought on. So the fact that you did it at all is something to be pleased about.
This is just a personal opinion thing, but in my experience the RS where you are learning doesn't always do things "by the book", now whilst this has it's disadvantages (it wouldn't be entirely unreasonable to say that it was a little unfair to put you in that situation on a lesson you are paying for), it also has its advantages in that you do get some exposure to situations that are a little non-typical of other Riding Schools, it's usually only by being in these situations that you learn to be confident in them.
Personally, I found that learning in that environment I was much calmer in the sharing/owning horses stage and have always been able to deal with stressy situations quite well. I'm not saying that it's always the best way to learn or that everyone should learn this way, but it had some long term benefits for me.