Ya know what I think .... I think that it was a mistake to contact wife when you took your kid to the urgent care. Let her find out after the fact.
Listen, your email "released her." Yet by calling her to tell her you were at urgent care, you "caged her" again. Your attitude should be, "Oh, well, this is what you wanted. You want separate lives? OK."
IMO, your calling her was a way of enabling her. It showed her that she can do whatever she wants and her "connection" to her girls will not change.
I say go "scorched earth." You need to show her the connection will change.