Yummy I am really sorry to say this but most men who abuse women start off like this.
He will be very remorseful. That's almost always the case. Sadly, it doesn't mean he will stop.
By staying with him, you will be asserting that this behaviour is Ok with you as long as he says sorry afterwards.
I'm not sure that's a situation you want yourself and dd to be in.
I fully understand how difficult this is and how shocking, because in order to protect your status as someone happily married and living together, you are going to have to sacrifice your potential safety and that of your daughter.
It's not fair and that's not your fault.
What you need to do is speck to womens aid. You need to write down, report and document every single incident, whether verbal, physical or emotionally horrid.
Womensaid can talk it through with you, clearly and sympathetically without taking any action on your behalf if you don't want.
They can advise you about sorting out come counselling or therapy for your DH, and tbh if he was brought up with vciolence he is fairly likely to repeat it unless some intervention happens.
You need to get even more support from outside - tell everyone, your folks, all your neighbours and friends if appropriate. They need to know the risk you are taking.
You could leave for a while or ask him to - better him, as unfair on dd otherwise to be uprooted.
Tell him he needs to see his GP and get therapy NOW because you are not going to accept him back into your home unless he gets some help.
At some level he has learned it is OK to hit women - how did his mother react in the past? He may not want to be like this but he can't stop himself no matter how much he wants to.
I would suggest trying to get your head around asking him to go for a few days/weeks or however long it takes. Zero tolerance is often the only way, or he will think you are ok with it.
Does that make sense?