Okay, this sounds all far too familiar to where I worked this summer. In short, we leased 15 horses that were not trained for trail, or for children to ride them. And they were taken on trail, with children. It was a dangerous situation on top of a dangerous situation.
You really have two options. Pick a horse that you can ride and you can care about, and try not to worry about everyone else. Its tough, but at you know that "your" horse is being taken care of. Or you quit, which is what I eventually did, since the only thing that my company cared about was taking the horses out on trails, even when we tried to train the kids to ride the horses, even when the horses were lame. Only thing those horses were there for was to go on trail. Someone needs to get hurt for them to understand that this is dangerous, and you need to open the doors and just not care that that will happen (yes, it really came to that for me... terrible isnt it?)
It would be plain impossible if you try to get a novice rider to calm down an excited horse. We all know that horses can sense their riders, and most novices are clinging on with their legs and arms and that idea will just make the horses more nervous.
In regards to your question (please don't disregard what I said about the danger part, I ignored what people said too)
You need to put that horses mind on something. If your going and he is prancy go in serpentines, even weaving up and down the trail. Keep his mind engaged, its really easy to just go along for the ride when working with trail riding horse. See if you can get him collected under you - fiddle with the bit, does he respond? If your horse is nervous, he needs some stability - he needs the same rider, he needs the same routine when you go out on trail, he really needs a confidence booster. Having new people all the time, usually screaming kids, and chaos doesn't help these types of horses. He needs a rider that will help him through it - if you can, I would suggest this horse be the one you stake a claim to. He may be a challenge for you, but you can rest assured that his problems are being dealt with and he will become a better horse because of it.
Good luck. If if the dangerous outweighs the safety, quit. There will be no way to cover your *** if something happens on your watch.