I wouldn't be able to handle it.
BUT:
She said she doesn't want me around the child and he won't have overtime stays etc.
She doesn't get to have her way there I'm afraid.
If you do think there's even a chance it could be made to work, that's one thing I would be setting out right fucking now.
When the baby is born, he applies for a court order immediately, to set contact, because there is no way on earth that is going to be at the whim of the mother. If he wants to stay married, he keeps that shit from your door by paying for a legal agreement. And yes, that will absolutely mean that contact - if it is to include your children - WILL be at your home, the mother will NOT have any say over how you and your children interact with your husband's child in YOUR own home. If he isn't prepared to take that bull straight by the horns and take absolutely no shit, then he goes, and he plays silly buggers with her from his flat. And you and your children won't be involved at all.
You and your kids come as a package. Don't agree for one instant to any sort of arrangement which has your children in it and cuts you out. I suggest you tell him right now that that ain't happening. Your children are going to be really affected by this and the last thing they need is for it also to represent a schism in their family - mum has nothing to do with this new baby sibling and never sees it? Yep that's really not going to fuck with their heads even more, not at all!
Time to address that one first. He wants to keep his marriage? Then he prioritises first, contact with the child, second, he prioritises you and his existing children as ONE FAMILY PACKAGE.