The good thing is that your husband backed you on this. I really think the sister in law is over reacting it isn't something that involves crying and calling every being the victim unless you've done something wrong and need support to spin the story.
Again you left it open to talk when she was ready to calm down and act like an adult but you were diplomatic about it. You took responsiblity for your emotions.
You are a writer of feelings you that may be your way of expression. If she is mature enough to see it that way.
I don't know how close you are to the ex but i wonder why you included her?
I don't know how mature your sister in law is but maybe in time she can see that you do a better job at writing your emoitions. A phone call or a coffee might have worked better in her opinion. She might be hurt over the fact that you chose to write it out. that she was not worth the time to sit down and talk it out. Once the drama settles i hope you work it out.