This sounds like a case of total laziness on his part. Younger kids are harder work and he's not interested in parenting the baby/toddler.
Even when your SD isn't there, he ducks and dives to get out of it. I bet he was like this when his oldest was little and now, history is repeating itself.
You need to have a talk with him and tell him the pressure it puts on you too be parenting by yourself. He's not stepping up. Tbh, I think, like many men, he sees it.as YOUR job and had no interest in tending to your daughter.
He also needs to know, that this will affect his bonding and relationship with the 16.month. old. She won't see him as a place of safety or have a close bond with him and may reject him.in favour of you, if he does try and do stuff with her, because she's not used to him. Then that will be more of an excuse for him to back off.even. more, if that's possible.
Don't make it about SD (or you'll get accused of allsorts), but about his presence in your child's life.
Forget SD for a minute. If he was the same as he is with your existing child, in terms of what he does, would that be acceptable to you? Would you have bothered to make a post..even on the parenting forum or anywhere else?
Focus on the actual issue. He doesn't step up at home with your child, but it seems like it annoys you more, because he steps up for his eldest. It's because he has to, now that he's not with her mum.
I was going to say that you shouldn't have another until this is sorted, but a pp mentioned your expecting number 2. Be prepared to be doing it all or most on your own, unless you get through to him.
Good luck with everything.