Please don't change your moniker its a fabulous bit of Australian yore. Love it! Thank goodness you clarified Old B because I was thinking Old Bitch but Old Bastard lets me know gender.
I did not use OB that is a type of physician but its also a feminine hygiene product in the US.
So the rescue let you have the dog but now they want to take her away? I would be wary of their assessment skills. Do you like the dog? I don't understand your problem I guess.