OP, I think your sister is being staggeringly unreasonable and inconsiderate - I'd say even narcissistic. And the emotional blackmail/ drama .... all while you have a new baby, and oblivious and completely uncaring towards your DC's needs, never mind your or your DH's comfort.
Frankly, you'd be well justified to saying YOU will never forgive her or get over it if she doesn't stop this crap right now.
But I know you probably won't do that, because you sound like a pleaser, who has spent their whole life bending over backwards to compromise and please her. I'm saying this with empathy, as my instincts are the same.
Trust me- the kind of person your sister is does not get easier from this behaviour. They just become dictators, everyone else always treading on eggshells.
I feel sorry for your DH- he's trying to give you some of the firmness you lack. But he really shouldn't be stuck in the middle.
YOU would prefer not to bring your DC. Your DC would be happier not going. And it's your DSis. It actually shouldn't be for your DH to negotiate. I understand you've just had a baby, but I bet this has happened before too? If we switched the genders here, and say it was a MIL causing an issue, we would classically say 'you have a DH problem.' Because it is the biological family who should sort this stuff out, not the person who is the in-law.
This really should be your job to be firm, not your DH.
I understand that in the circumstances, with your energy depleted from new baby, and the escalated feelings of the wedding, maybe you will feel you have to go for compromise this time.... but I really hope you break free of your sister's spell soon.