OP,
This is not a good situation.
He is an angry bad tempered man and your child is becoming confused and nervous of him, with good reason.
He has zero patience.
He is a big angry man and she has now recognised that she is not safe with him.
You are shoring up real problems going forward if this continues.
Do not get pregnant again with this man.
He is deeply critical and unkind to a small child and yet is surprised the same child is now backing away from him.
If this continues, she sounds like a child who might mention that Daddy is very angry at me.
Anyone who hears that, will report it.
Parenting is not easy, parents get frustrated, but this is all the time and all his interactions with her.
You have a real problem.
Personally I wouldn't trust him around your daughter.
Stop him doing the bed times, because he is damaging your child.
In your place, I would furious that he is behaving like this and I would be rethinking the relationship.
His behaviour will not improve if you allow it to continue.
This behaviour is not normal.
Men like him make children nervy and anxious and that will stay with them.
You are 100% correct to be very unhappy with this.
Protect your child from him.