I think that sounds like a very good idea, Always - one step at a time.
And for what it's worth, life with this man has totally recalibrated your idea of 'normal' so that it's WAY, way off.
It's not normal or right for a partner to push you.
It's not normal or right for a partner to grab you.
It's not normal or right for a partner to scream at you.
It's not normal or right for a partner to hit you in any way.
It's not normal or right for a partner to do any of these things to you in front of your DC.
None of these things are okay. None. Zero. And none of these things are things that good men, loving men, supportive men, caring men - do to their partners.
Have you ever heard of the "boiling a frog'' metaphor? I don't think it's scientifically accurate but it's useful, and it goes like this:
If you drop a frog into a pan of boiling water, reflexes kick in and they jump right out again.
But if you put a frog in a pan of cool water and heat it slowly, one degree at a time, they tolerate the increasing heat until they've boiled to death.
He has turned up the heat so much that he's made you accustomed to it. He's treated you (and your children, by extension) so badly that you think hey, it's only a push. Only a shout. Only a yell. Only a hit-with-the-heel-of-his-hand, it's not like he broke my nose or anything... I'm sure you didn't think, on your first or second date with this man, "oh, I think I'll stay with him unless he breaks my bones." I'm sure you thought you'd have a happy, normal life together. But you don't - this isn't normal. It's not what 'all marriages are like when they go through a rough patch. Actually, the water is almost at boiling point.
Well done on telling a counselor, well done on telling your Mum. These are important steps - but they may not be able to swoop in and rescue you. You may need to move out, or get him to move out - all by yourself. It's worth doing, because your DD shouldn't ever witness what she's already seen.
Take care of yourself.