Ugh - sounds like a really awful situation.
I think your letter sounds really nice, but because the clients are your neighbours I think I would be more inclined to phrase it a little differently. As soon as the parents read that their son has behavioural issues they are going to get defensive and, based on what you wrote, they will blame you. Personally, I would bow out of the situation with as little drama as possible. If I was in your position I think I would talk to them about it tonight and say something like, "you know, I really like having you as clients and I think Sam is a great kid but it is not working out. He isn't getting along well with the other children in the group and as you know has hurt them. I am not able to give him the care that he needs while maintaining the safety of everyone in the group." And then I would write a short and concise letter outlining that as of XXX date you are no longer able to provide care for Sam.
Does your contract address termination? Do you have to give notice?