@DontKnowWhatToSay25
If you are absolutely determined to believe and forgive him, then the best thing that you can do is close the door firmly on the episode.
Don't contact your friend or her husband.
If your mutual friends still see them, there is nothing you can do to stop that.
Yes, you can ask them not to do so but some people will react badly to being told who they can and can't see because of an incident that has noting to do with them, so best not to ask in the first place.
If you all socialise in the same place and it really is very painful for you, then you will have to change where you socialise. In extremis, you and your family can always move away.
But stop thinking that you have any control over the woman, her spouse or your friends.
You do have control over your reaction and if you want to move on with your husband, then you are entitled to do that. But by dragging friends into it, sending letters, you are making the whole business into a sideshow and a fruitless sideshow as you cannot issue commands.
People will laugh at you, it will become even more of a talking point, a scandal, Discretion is your friend. You have decided to stay together-if anyone asks what is going on, just say-it was a bump in the road but onwards and upwards-play it down.