Netty, teaching an older horse might prove difficult, from what you say she is set in her ways. I'd certainly suggest that you sent both the horse and yourself to learn the American way together.
Yes the show is a place to start - put yourself about and ask a few questions.
Whenever I have been around Western riders in the UK - and there are quite a few - I have usually come away with the feeling that the social side of things is as important as the horsey side. And they do like dressing up.
As for herding up your cattle, well, I tried it once and nearly died laughing.
We eventually went and got the tractor. Our British cows aren't exactly American steers but luckily they don't have horns either.
One thing Netty. There is no reason why an English rider can't sit on a Western saddle and ride the horse. The saddle makes it easier.
And remember any horse you ride will pick up on your nervousness.
It sounds to me as though you need to meet a placid pedigree Dales pony - that's just down the road from you.
Mind you they can be expensive but one might look after you. Don't worry about the height - they were bred to carry lead across the mountains.