I have been through this with the 'other woman' but she was also the other woman who behind my exs back wasn't interested in the children, only to his face so it was very difficult to deal with. Mostly, the children didn't know whether they were coming or going. At one point my then 4 year old asked me what a 'fing dirty slg' was and when asked why he needed to know that, he said that was that 'other woman' called me when daddy wasn't there.
You kind of just have to hold your head up and ignore the provocation. I find reducing my contact with the ex helped enormously and it is far easier to see yourself as a family unit - just you and the children - and deal with that than it is to try and include him in your decision making or emergency plans for childcare or anything else. Being self-sufficient in every possible way reduces the need to have to deal with either of them. E-mail him rather than speak to him. Never pick up the phone unless it is a genuine emergency. If the e-mail you are sending is being sent in retaliation to one of his that has annoyed you, wait 24 hours before sending your response. The chances are you will send a very different response then. Focus on the children and nothing else - your relationship is done, he is with her now, that is not your concern.
You should also realise that this is her issue, not yours. She has a man she doesn't trust. For reasons beyond me, they seem to think that we see in the ex the same thing they do - and for me all I see is an aggressive, abusive man I would no longer touch with a barge pole so I won't be fighting her for him! She, however, is threatened by your relationship and the need for you to continue a relationship, albeit a very different one, for the sake of your children.
It is also easy to say but be grateful that she is generally nice to the children because trying to deal with your children being slapped across the face by the girlfriend is very, very hard (been there, done that). You will probably find that given a bit of time, things will settle and she will be less defensive - the more you battle her, the longer that will take. Take as big a step back as you are able. Before you open your mouth think about whether the issue will matter in a week, a month or a year's time. And if it won't, just ignore it.
Facebook blocking is good. You don't need to see that and frankly, why would you open up your life to your ex's scrutiny? Give yourself a break!
Be kind to yourself. These things are hard to deal with and take time to come to terms with.