I am so sorry that things have went further down hill for you. But on the other hand I am glad you felt you could come here for someone to talk to.
I think your actions are correct.
First let me applaud you sticking up for your children and telling your wife her treatment of them is not acceptable. Since you are all they truely have to buffer and sheild them from her behavior.
Second let me applaud you for not cowing down to your wife. And not allowing your self the room to get sucked into her blame game. By keeping it short in affirmation of your wants and not doing the pleading thing.
I know your wife is sick. But I do see maybe some good will come from her leaving if for no other reason then to give you some space and her some thinking room. (I do hope you informed her the dogs go with her on her departure). Have you spoken to her doctor about this latest event and what approach he feels you should take?
I really have nothing to offer you but my heart felt prayers that you and your girls get through this unscatthed. Which I doubt is the case.
She did admit to having made at least one mistake, “adopting that little [censored]!!!!!”
This really bothers me that your wife said this. I hope your daughters were not in ear shot of this comment. No matter how in the heat of the moment it is those words will be forever etched in the memory. You may want to think of how much more rejection and turmoil they are going to be able to endure with out it causing damage that cannot be undone. As is in your wifes case.