Thanks for your observations and reassurance - a few comments:
a. aside from the leader and support, these were really quite small riders - a good riding school will give them only the most placid horses to ride, a not so good school might take a chance with a slightly flightier horse
b. I agree with the cheery hello, but 30 metres is quite a long way away anyway, and in this case there was a strong wind against, so it would have been difficult to make myself heard unless if I had shouted at the top of my voice, which might have defeated the object
c. if this had been a trail not a field, I wouldn't try to overtake, but nor would I think it necessary to hang back 30 metres - 10 metres seems enough to me, if the horses are fit to be ridden by small children.
I agree with the view that some horseriders seem to feel superior, partly because they are wealthy and partly just being so high off the ground and literally talking down to you. But on the other hand, the majority of horseriders are the most considerate and civilised of all the users of the countryside in my experience.