WTBH, I really, really, really want to take that woman by the shoulders and shake her. And then the system that employs her without providing training about the situations she's likely to encounter in the course of her job. OMFG...
I am so, so sorry that she not only invalidated the harm that it does to you and the girls, but then accused you of provoking him. Here's what I would need after hearing that from some one who was supposed to help:
NOTHING you did or did not do warranted his behavior. YOU are NOT the cause of the abuse. It is NOT OK for him do this. It is NOT OK for your girls to be so afraid of the fall out that they are ALWAYS OK. They should be able to feel, to have bad days... they shouldn't have to be perfect every day, every minute just to ward of something bad happening, so they aren't the cause of their father's anger.
You are an amazingly strong woman and a wonderful Mom!
Hugs, hugs, hugs and / or maybe holding a punching bag for you while you let go of the anger and frustration caused by her ignorant comments.