I'm sorry anxiety is horrible to go through, I experienced it for a long while after my divorce. Anxiety is your stress reaction to the events and you need to deal with the physical symptoms before you can get down to the nitty gritty of dealing with your wife.
So there are some breathing exercises you can do but these only really work when you start to feel the anxiety. One is breathing in through your nose and out through your nose but imagining the breath running through your lungs in a circular movement. The other is singing. Singing not only distracts you but it also regularizes your breathing, so find a song that you can sing to yourself once you feel your anxiety starting. It is all about nipping the anxiety before it builds up to the big crescendo. There is a lot of cognitive behavioural exercises around this, and books you can read which give good techniques.
With regards to your wife. Whilst it would be really nice to respond and tell her exactly what you think, it sounds like she is trying to provoke a reaction and it would make her respond with more. Also not nice for your kids. I would journal your thoughts and reactions, get them out of your head. Keep a book where you can release this stuff and then when the time is right and it is done and you are happy destroy it. It will be very liberating. Really talk to your wife in it, tell her how you feel and how she is making you feel.
Secondly, you could get another phone, one for everyday messages and one for your wife. That way, you know when that phone goes the message is from your wife and you can choose when to read it and mentally prepare yourself, it gives you back some of the power, even if she doesn't know it.
Finally, this is *her* problem, it is not yours. You could not control the divorce, it happened but now it has you have an opportunity to live your life. Don't let her take that away. Be your own man, be a good dad, the only person you can ever let down is yourself and so far, it seems, in not responding you haven't done that. Well done.
Keep going, it does get better with a bit of practice, re-training of thoughts and time.
