hi there, I know nothing of the issues behind this letter as i have not seen the previous threads but can i make the following suggestions (i hope i am not too late!)?
I think that with a letter like this it is a good idea to state the tone you are trying to achieve. A sentence at the start like: "obviously it is difficult to be sure with the written word that it is being read in the tone it was intended to be written as things can be misinterpreted. We can assure you that we are sending this letter in a real and unconditional spirit of reconciliation and hope that it comes across as such."
also, you are already showing yoourselves to be big by sending the letter and I think you can reinforce this further with a sentence like "whatever the rights and wrongs on both sides, we really want to move on. Obviously we cannot speak for you but we can honestly say that where we have messed up and caused any hurt, we are unreservedly sorry. We don't want to go over old ground, just recognise that much has been said and done and show that we want to find ways to move forward with you"
finally, I know it is a cliché but if you can find a way of saying that life is short, I always like sentiments like that. Without be patronising to them, it would be no bad thing to remind them how much everyone would regret this feud when life moves so quickly.
Finally, i am not sure about the word "nice" when saying it would be nice to hear from you. It doesn't sound convincing or warm enough. I would be a touch warmer with something like, "look, we really would very much like to hear from you, for all the above reasons and more, and try to find a way for us to all move forward together and leave this really difficult situation for us all behind"
hope that helps and good luck