"I want a 'Batwoman' to have an equivalent mission to Batman, not to be chasing looney relatives"
When was it established that Batwoman just wanted chase looney relatives? Her mission for all intents and purposes IS equivalent to Batman. Stop the bad guys, save as many as possible and be special! All we get is that one line "You have our father's eyes", that's it.
"What was I thinking?"
You weren't. We still don't know what the end result of this story will take us so I wouldn't jump on judgement that Batwoman's story will lead into dull mediocrity just because Alice may turn out to be her sister/half-sister.