I really appreciate all your advice. Thinking about all the options you've presented, I'll clarify that these kids rode on a lead line last year - rode one of the "ancients" - the babysitter mare - and on my good gaited horse because the 2nd ancient was going through a thin phase and it was hot; we didn't want to stress him out. We didn't put the kids on the lunge line, though, which would be a great (new) learning experience for them and would allow us to do trot and/or running walk with some speed in a controlled way. I did make them groom the horses before they got to ride last year, and they did not want to do that at first.
It turned out that they were afraid of them...so we took a step back and spent some time introducing the kids to the horses. It turned out good and that they saw that the horses appreciated the brushing and rubbing. I will need to check into the halter/bitless bridle idea, and I may use that on the lunge line as some of you suggest to see how they do in balancing themselves.
I am thinking about the progression of these lessons. I expect that these kids will be recurring visitors throughout the summer, so this will be kind of sporadic. Does this plan/sequence make sense? First, we will do lunge line without reins (balance). Next, we would want to introduce the bitless/halter idea, with reins to see if the kids can control the horses with reins, seat and legs (control, confidence, good hands). Last, if we get that far, we would tack up with bridles with our mildest bits. I am keeping all this in the round pen and/or our arena, which is smaller than a competition size.
What do you think? And, thanks again - you are giving me a lot to think about!