That isn't how family courts work, Far. You can't have something thrown on anyone. What happens is that both sides write a position statement, and then have a chance to reply to the other side's, setting out their version of events the other has claimed. And allegations of domestic abuse are set out on a separate form, too. So neither side can ambush the other at all.
Don't be scared of his solicitor twisting things. The reality is that judges in family courts are solely interested in the interests of the children when contact proceedings are at stake, and they will know that intimidating your child's mother so you can try to grab material possessions she has receipts for, after harassing and bullying her endlessly, all in the presence of that child, is not indicative of great parenting.
A non-molestation order isn't actually that easy or automatic to get, and nor is a place in a refuge, and the judge will know that. Your ex can twist things all he likes, you have evidence in spades of his behaviour and you've acted to protect your baby from him and his family until a safe contact framework can be set up. A non-molestation order will keep you safe and able to catch your breath and the court will look at how to ensure contact isn't harmful to your dd.
You're still scared of him, of his power over you. But he doesn't have any. All court action will be about is how he has contact. That's it. There's nothing he can do to you. You don't have to see him anymore or deal with him again, and you're really likely to get brief contact centre contact to begin with, too, so you don't have to be scared about him taking her and leaving her alone with your MIL all day either. You'll get a residence order so he can't take her from your care, and a schedule for contact will mean you know what the pattern is and can plan for it. So he can lie as much as he likes and try to make out you're the baddie all he wants, the judge is not going to give a shiny shit. The judge doesn't care who the baddie is. He or she cares that your dd has contact in a safe way with a parent, and that she has a secure home base. So all he'll do if he rants and is angry is look who he is - someone incapable of putting his child's interests first. Let him lie. He can't lie his way out of all he's done in front of witnesses - ffs you needed a police escort into your own home on moving day, after which he sat there in the road in his car trying to scare you - and your friend was there when he tried to break in to steal property you had receipts for from you. That is not normal behaviour. None of it is.