Barbara Kean and Tabitha Galavan's relationship was actually really good. However, it wasn't until the death (or should I say murder) of Butch, who was also in a relationship with Tabitha, that things went extremely downhill for the couple once Tabitha found out it was Babs who killed him.
Dysfunction at it finest, I would compare the end to something along the lines of Harley Quinn and the Joker. Which is not surprising since it's hinted that in Gotham's upcoming fourth season Barbara may become Harley Quinn. It will be interest to see how that will happen especially since she is supposedly dead (in a shocking twist murdered by Tabitha). But death is never really permanent for some in Gotham City.
I wonder if these two will gravitate towards each in some sort of capacity because like Harley and the Joker no one does dysfunctional romance like them or is this officially the end for these two?