T.H.
I really feel for you. You are in a hard situation and one I have seen way too often. My husband is a divorce attorney and this is very common in divorces. That's the good news, unfortunately you will be the one with the hardest task. I feel the ex-wife is jealous of you and she in return is attacking you out of her own insecurities.
My advice to any of my friends would be this: you will have to learn to say "oh" or "oh really I'm sorry you feel that way" to her comments. This way you will not have to engage in an argument or discussion. This may sound easy to do but it is extremely hard, because what she is saying hurts and you will want to defend yourself. There is a saying that misery loves company and if she can make your family life or you miserable then she wins. By saying "oh" it does not leave any room for further discussion and you are not agreeing or disagreeing with her.
In with regards to the children, I would sit down as a family and explain to the children that sometimes when people are hurt they take it out on someone else, even if that someone else did nothing wrong. Which it sounds like your step-son is beginning to realize his mother is treating you on fairly. By responding with “OHHHH” to her “I hate you” e-mail you will not fuel the fire and your step-son will respect you more for it. You may also want to give some examples to the children through the children's own experiences of the world. For example when a friend was mean to them and why, or my own son will take his frustration out on his sisters if he has had a hard time at school. Then we sit down and figure out a way for him to work through his emotions in a more positive way.
In addition, I would have your husband be the one who responds to her e-mails and phone calls for awhile. With everything else us mom’s have to do the ex-wife would be way to overwhelming for me personally, so I can only imagine the energy this is sucking out of you. If you can step back or away for a couple of hours (a weekend would be better) it would help restore your energy if you are feeling low. Try to take care of yourself and take breaks from the situation as much as possible. I wish you the best of luck and I hope this helps.