OP you need to step away from the ex situation.
She’s obviously got her own agenda but it is not your cross to bare.
Your OP agrees that the kids can’t be there when he is not home, that is all that matters.
If the contact order is in place and it is EOW then that is what should happen. If he and his ex come to some additional arrangements then good for them and good for the kids but it should NOT fall to you to do the childcare, especially when you are not even a month post partum.
If the ex wants different contact then she will need to seek a change to the contact order via the official channels.
It sounds like your DH is saying and doing the right things. Please just let him deal with it, the emotional impact of a new born is already life changing, don’t take on the emotional strain of trying to sort your partner and his kids out too.
And don’t let anyone on this board tell you it is your responsibility to look after someone else’s kids, whilst many step parents do this off their own back and enjoy it, many do not want to. Me included. Throw in a newborn to the picture and I felt exactly the same as you. Overwhelmed and resentful. It’s not the kids - it’s the interference and insistence of the ex.
In my case it was the insistence that the SC had to be brought to the hospital when my newborn was in NICU and incredibly poorly. I wouldn’t have brought my own children but because the ex wouldn’t stop calling and messaging they had to be brought over.
Still haven’t forgiven it to be honest.