GoldenR
You and I've had different takes on things over the years, but I've always though we are kind of alike in our morals and values.
You,my friend, know the answer and probably what you plan to do. 
The statement your ex is mentally unwell is the understatement of the millenia. The odds that she gets better any time soon are small. November of what year? j/k.
I know you love your kids and while it might suck for awhile. . .Just picture your daughters face if you all got together. I get that outcome has merit and understand the payoff to you like only another father could.
Look it is your life and I know you well enough to know not to tell you what to do.(BTW I am like that too).
So what is the harm in trying to figure out what could be put in place that minimize the chance at it being uncomfortable or turn into a ugly scene?
Look, clearly you are thinking on this and sometimes once the anger is released it leaves room for cmpassion/pity. I can tell you that releasing yourself from a burden can feel really good. Being angry at someone that shouldn't matter to you seems pointless doesn't it?
BTW anything you want/need to agree to a joint Birthday party you are likley going to get from most parties.
Everyone involved understands your view and also how much pain your ex has brought to everyone she ever knew.
Imagine the respect you would gain from everyone involved showing an openess to the idea.
Forget what it would mean to your Ex (based on your descriptions I am not sure she has a soul).
Everyone else including your current wife would respect for thinking of others before yourself. Sometimes we have to feel weak so we can remember what strength really looks like.
You can chant or sing kumbaya if you want. Your call. 
Good luck with whatever you decide.
