Not allowing them to come to the hospital probably wasn't your finest moment tbh. Sorry, but I think on this one you've got to see it from their point of view.
In terms of everything else, she sounds extremely controlling and patronising. No one can demand respect they have to earn it.
There's a big difference when a MIL or indeed a mother that can see you are exhausted and struggling and but HELPS you in a practical sense (takes baby out so that you can get some sleep etc), as opposed to TELLING you what to do. That would just p* anybody off.
She's already done her mothering duties with her own family and now she wants to with your baby.
In her eyes, when do you actually become the mother I wonder?
With regards to your DH, this is actually blackmail, and personally I can't see how that would work - do you believe he would carry this threat out?
Sadly you are out-numbered, and I hope for your sake you have some good supportive friends in RL because I think you are going to need them. (Mother and baby groups are great for this - you'll probably find one or two that are going through the same as you).
I think you need to offer another 'peace' meal and get this all out on the table as truthfully but as tactfully as possible. If they are the type to hold grudges, there is honestly not a lot you can do. Sadly you can't force them to see your DS, but hopefully they won't cut off their noses to spite their face.
Good Luck!