My ex was found in contempt recently for parental alienation. I recently found out she posted a blog about me with information about our marriage and it’s deterioration and details of the divorce. The blog indicates her dis-satisfaction with the NC court system for finding her in contempt, in the blog she she makes defaming and slanderous statements about my conduct and the NC courts system. The blog can easily be found by the children since they are teenagers. The permanent custody order states that " Neither party shall attempt, or condone any attempt, directly or indirectly, to estrange the children from the other party or to injure or impair the natural love and affection between the parent and child."

The ex has a long history of being admonished by the judge and has been ordered to undergo anger management. Is it appropriate to file a motion to show cause for this latest event?

I would think so, yes.

what if I do not have absolute prrof that she posted the blog?

You can still file the motion and argue that she is the one who posted the blog.

My ex has removed the blog is there need to file the motion to show cause it was active for 7 months without my knowledge.

One thing you could do to try and retrieve the blog is to use the "wayback machine."
It can be useful to show what use to be on a website even if it is no longer around.

If the blog is no longer active there is really no practical reason to file the motion at this point.