"Surely a divorce shouldn't mean that you can no longer choose who your kids get close too?"
Newsflash. That is EXACTLY what it means. Both parents have the right to bring the child up in a way they feel is appropriate, provided it's not endangering the child. And ffs, a woman who was a worry would not bebe most unlikely to be anxiously posting on MN asking how to negotiate with her dp's ex so she can get to know his child. That's the action of a decent, concerned, and responsible adult. Not to mention the fact that the mother has never even MET the new stepmother and is trying to avoid doing so, so how on earth is she placed to form a view?
Your child is not your property. I'm startled at how many people fail to comprehend this fact - you have a duty to them, not first dibs on them! They have their own needs and interests, and (agonising as I accept this can be) a good relationship with the other parent and any new dw/dh is pretty high on the list, unless they're toxic. As a parent it's your job to help them achieve this, and to soothe any anxiety about guilt and betrayal they feel.
My mother did this magnificently. My father tried to get us to take sides - and then did exactly the same to my younger half-brothers, when he left their Mum, despite DH and I trying to tackle him on how appalling that was of him. Guess what? As adults, all his kids pretty much despise him for it. Nice harvest to gather in for the future, hey.
Finally, on one level she should be relieved. Plenty of stepmothers are marriage-wreckers, many more resent and exclude stepkids; the loving, inclusive and welcoming type, appearing on the scene post-breakup, should be a godsend. Nobody can replace a parent, but a child of a divorce can gain hugely from loving and involved step-parents - if the adults involved behave like adults.
OP - I think working on meeting her and asking how she wants to handle this is best. Agreed she is being incredibly difficult, but negotiation is surely a better bet than court orders, if at all possible. The latter tends to start a war, with the child the front line.