A 9 month old that will not be put down & just wants you is draining. There was 'An Incident' that, when I think about it, still scares me.
He called you, not jokingly, a cunt. Unacceptable. Even if used jokingly at other times.
He pushed/barged into you.
He called you LAZY when YOU are dealing with a grizzly 9 month old, sleep deprivation & doing all the house work.
You lashed out & hit him. I'm unsurprised. I'm not saying it was great, but unless you're a lot bigger & stronger than him, or hit him in the face, I don't think the world us ending anytime soon.
It's good you've both apologised and hopefully you can talk about it properly tonight.
He needs to explain where 'You're lazy, just swanning around with the baby' came from, because saying sorry is not enough. The underlying resentment from both of you will still be there if you don't get to the bottom of that comment.
You both, especially given your previous abusive relationships, need to resolve not to ever lash out physically again, no matter what. No Matter What. Walk away. You both need to feel safe, not scared. His barging was as bad as your hitting.
You need to discuss what language is and isn't acceptable in anger. I, personally, think calling anyone a cunt or whatever isn't acceptable, but I have no objection to swearing. I'd say 'That was a fucking stupid thing to do!' But I'd never say 'You're a cunt'. (Unless in jest maybe, thanks to MN,)
You need to discuss your fears around DD's health.
You need to discuss him doing his share of looking after her & his home. He needs to be pulling his weight. He works, you're a SAHM. They both stop the minute he comes in the door and you are BOTH her parents and you BOTH live in the house.
I suggest you go away for the weekend (quiet hotel if you can afford it, or family, friends if not) and sleep, read, whatever. Leave him a list of jobs that need doing (the stuff you do daily) and give him a taste of 'being lazy swanning about with a baby). DD will cope just fine. It's her Daddy, not an alien, if you aren't there she'll be perfectly ok wth him looking after her.
Don't sweep any of this under the rug, it'll only continue to cause problems.
Oh & sort out whatever started the bickering this morning!