Re: DC's New 52: Reviews and Discussion (Spoilers welcolme and likely)
Not necessarily. The only time I can recall Batwoman really working with the Batfamily is during the Blackest Knight story, which was while Dick was under the cowl. Someone as close to Batman as the Joker would see very clearly that Batwoman is not associated with him the way that Robin, Nightwing, Batgirl, Red Robin, etc are.
"In Brightest Day, in Blackest Night, no evil shall escape my sight. Let those who worship evil's might, beware my power: Green Lantern's light!"