I agree that it's unacceptable and needs to stop, but if it's a sudden change in behaviour (from your partner), I'd try to figure out what's behind it. It's still unacceptable, but also quite possibly fixable.
Is there other stuff stressing him out and he needs to work on his self-care/stress management? Is he actually unaware of what normal toddler behaviour is like (or has forgotten, depending on what your eldest was like as a toddler)? Is he parenting DD2 as he himself was parented (although I'd ask why he's suddenly started doing so)?
Yes, ideally he'd do this thinking himself, but sometimes we can't see or think clearly when we're in the thick of it and need a bit of support – it's your judgement on how much you can and want to give. (And you can only help him identify the issue and some possible solutions – he has to actually do the work to fix it.)
Sometimes having these conversations separate from any specific instance can help, so emotions aren't always running high. Or presenting the behaviour management as a joint thing, DD2 is getting older, she's starting to do X, what do you think, shall we approach it this way or that way, so that we're on the same page?
Alternatively, is there someone else close to him it might help him to have a chat with, his mum/dad, sister/brother, best mate?