No I would not be ok with this.
If you and DH was struggling and the girls were stood there laughing at you, then I would understand your frustration.
But it was you and DH laughing and your girls just joined in, they were literally doing the same thing you were both doing - but yet they got shouted and pushed for it.
How can you shout at them for doing the same thing as both of the adults are doing.
I do understand being at the end of your tether but there’s no reason to shout/swear or put your hands on a child.
I’m struggling to understand why he’s so stressed out over it when there are 2 of you?
Why were you both trying to get her in the bath?
No wonder she doesn’t like it.
It only takes 1 of you and if they’re getting stressed then you switch over.
If he was getting so stressed out that he shouted/swore and pushed a child, then he should have removed himself from the situation.
If he pushed the baby like this then he could have actually hurt her.
I would be telling him that this is unacceptable and you will never allow it again.
Tell him to recognise when he’s getting stressed and to remove himself before he puts hands on any of the kids.
Then I would get him to apologise to the older ones and you can say how his behaviour was completely wrong.
Is this your DH’s first child?
Kids are difficult but you’re both struggling way more than most parents do (that’s not a dig just a genuine concern/observation).