Honestly Op I don't know if I could or not and I really feel for you.
You said she's due in a few weeks, what has your DH said about contact? What's he hoping for?
I think for now I'd be firstly insisting on a dna test, is he open to this?
Contact when baby is very small will be difficult, it will be little and often and no he won't be having overnights etc straight away.
Regardless of your decision your life will change, your children will have a sibling and even if you split up the child and by default the mother are some what part of your life.
My advice and I realise it's easier said than done, would be to take a step back. Let him establish contact and a relationship with the baby (just him at first) give it a few months, continue working on your relationship but take talking about the baby, seeing pictures etc at a pace you feel comfortable with, same with telling your dc.
I think it's it's to work and there's no guarantee it will, but I think you'd maybe rather know you've tried. But it needs to be slow and steady, your DH needs to understand that and he also needs to think if that's something he's ok with.
Some other points worth discussing looking into.
Maintenance, definitely through CMS.
Solicitor regarding rights, contact. It can be done without too, so don't let finances stop him. I'd be insisting on a court order for contact.
His family, it's natural they'll want involvement, but this may be something he wants to delay until things are more formal.
Best of luck Op