I have witnessed many people in your situation that get something on their mind, and won't let it go until they follow through with it. The friendly photo of WW and OM was eating at you. Add it with the hypocrisy and b.s. you WW says, you were thinking how sending the photo would be a truth dart. And, you wouldn't let it go until you finally sent it. I see LBH's start thinking about baring their souls in a letter to their WW's. No matter how many people tell them not to do, they won't drop it until they do it.
Here's the thing. She gets you angry, and that is understandable. Nobody blames you for being upset. We are trying to tell you that reacting in anger is not how to interact with her. To her, it appears vindictive. The minute the conversation turns sour, that's the minute you discontinue the message. Make it a boundary. "I will not engage in a discussion where I am being disrespected" (lied to, cursed, yelled, demanded, etc.). Of course, that means you show the same curtousey.
If you really want to make a point, pierce her heart, or swing her head around..........then show no reaction whatsoever. Do not show recognition to her snide comments or b'tchy remarks. I don't mean you should act passive. WW's hate passivity in men. But don't engage her pi$$ing contest. You are above it. You show you are Fonzie cool, and she does not have the ability to ruffle your feathers. You won't give her that power which leaves you even more empty and flustered. Giving over to the temptation of pushing her face in it, or pinning her to the wall with truth darts.........would bring very little and short lived personal triumph, IMHO. When truth darts are given from anger, they get anger from their target.
Whenever she sends a nasty written email, leave it alone.......especially if it starts making you angry. Give yourself so many hours....or days before responding. If it something about the kids that needs an immediate answer, then take care of that business only. In fact, telling her that you think it's best to discuss nothing outside of the children is best for now.
You need to make a goal about how you interact with her, and what you will do if things take a bad turn.
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!