Mega fan of: Helena Bertinelli (pre-52), Batwoman, Birds of Prey, Guardians of the Galaxy, Secret Six
Fan of: Batman, Cassandra Cain, Wonder Woman, Silk, Stephanie Brown, Captain America, Hellcat, Renee Montoya, Gotham Central, King Shark
Quasi-Fan of: Aquaman, Midnighter, Superman, Catwoman, Nightwing, Green Arrow, Squadron Supreme, Red Hood
Other likes: Low, Hush, Arkham Asylum: ASHoSE, Watchmen, A-Force, Bombshells, Grayson, Unfollow
Team Cap (both Rogers and Danvers)
LOL. No worries about correcting me. I'm usually the one doing that to other people (ESPECIALLY IRL)
But yeah, I freely admit that I didn't read past the first couple issues of Kate's solo. It was really damn good, easily one of the best Nu52 titles, at least until the marriage fiasco, but the book just wasn't for me personally.
They discuss the Team every so often and occasionally advise each other. Also, being cousins, they knew each other as children.
Childhood (only depiction of them as kids together so far):
http://www.cbr.com/detective-comics-939/
'First meeting' as Batman and Batwoman (as opposed to Kate's encounter with Batman before she became Batwoman):
http://scans-daily.dreamwidth.org/6692459.html#cutid1
Cousin Reveal:
http://scans-daily.dreamwidth.org/6249628.html#cutid1
There's some good stuff at the beginning of the 'Victim syndicate' arc where Batwoman talks to Batman about him needing to grieve, and by the end of the arc Batman's telling Batwoman that's she's been closing-off and advises of what to do about it (I think it was the same arc). And in #51 they talk about taking Cassandra for an outing to either the Ballet or baseball (which of course gets interrupted).