Something that has worked for me is to understand the underlying issue that is prompting someone else to treat me a particular way. It sounds like you MIL is in a great deal of fear and the belief that drives that fear is: what others think about you is important and determines your worth. The question now becomes: Are you going to 'buy in' to her belief and fear? Or, are you going to allow her to simply be where she is and then allow yourself to believe something different?
We can respect someone else without 'buying in' or catering to their fear. Respect does not mean responsible for their well-being. It isn't easy to have someone constantly putting you down or verbally being mean, however, it is really important for each of us to learn to create the boundary of "This is where you end and I begin."
I have learned to listen to others that don't agree with what I say or with what I am doing and to avoid defending or justifying. I simply say: "I see that you are really upset with what I did." And I leave it at that. If they get loud or mean I literally put my hand up and say "Stop". I then say, "I will not allow you to speak to me that way." If I am on the phone I have actually hung up the phone at that time, if it is in person, I walk away at that point. All of this I do as calmly and non-confrontationally as I can. (Of course, then I usually call a friend or journal to vent or go have a good cry and respect my own emotional response to being attacked.)
We can't change other people's belief systems and the behaviors they have as a result. We can, however, take full responsibility for ourselves and choose response as opposed to reaction.
When your MIL gets upset about something like your screen name you can simply acknowledge that she feels fear about it and just stop the conversation there. If she continues, you can 'broken record' by continueing to say you understand that she is really upset by this and really in fear for her reputation. Drop the rope when you find yourself in a tug-of-war you don't want to be in. Stop trying to convince her of something else. Defending, explaining, justifying, convincing are all pointless. She obviously is in too much fear to hear you.