Don't send that - or at least wait 48 hours to let things settle and so you are really sure you mean it.
We are a loud family too. Things like you mentioned happen in our house also.......and I bet they do in most people's homes.
My H accuses me of being 'sharp' with the children and thinks I am angry when I think am not; it's all a question of how both people interpret it and how the children play on it. They sense the tension - and yes, sometimes they play on it.
Please wait before considering sending what you wrote. It is a knee jerk reaction because you are hurting at the moment. She is not the woman he wants to be with and so your letter will not do what I think you want it to.
If you want to give up do that, but there is no need throw the OW in to the mix in doing that.
I think the time to give up is when you feel indifferent to your H - not when you feel angry. Anger shows me you still have feelings for him. I knew my sister's M was over when I saw complete indifference in her towards him. You do not seem to show signs of that.
Give the C a chance to work on your H. You are still in the very early days of that.
Saffie me 46 H 46 M in 1986 D20,D18,S16,D13 H's A 01/05 to 07/06 H recommitted to M 07/06 renewed vows 09/06 Going from strength to strength