hmm well the Bat family right now is pretty different from the one you remember. if you are looking for all the characters that
have been considered the Batfamily between now and Post-Crisis, I think everyone has you covered so far but as for who compose the roster of the current Batfamily/active Gotham landscape let's start here:
so this is pretty much the current Gotham cast and likely who DC will be focusing on in Gotham for the time being. based on this, following would be considered the modern Batfamily
Batman/Bruce Wayne
Catwoman/Selina Kyle
Red Hood/Jason Todd
Nightwing/Dick Grayson
Oracle/Batgirl (Prime)/Barbara Gordan
Batgirl/Orphan/Cassandra Cain
Batgirl/Spoiler/Stephanie Brown
Robin/Damian Wayne
Signal/Duke Thomas
Red Robin/Robin(?)/Drake/Tim Drake
Huntress/Helena Bertinelli
Batwoman/Kate Kane
pets:
Batcow (I think he still shows up sometimes)
Titus
Ace
Goliath
then we have The Fox family who are currently going through their own developments and are very much Batfamily adjacent right now; but I will say that Batwing/Luke Fox is still tentatively considered Batfamily. I'd also include Bluebird/Harper Rowe as tentatively considered Batfamily because she quit for a while and has only recently started making a comeback.
Azrael/Jean Paul Valley should still be considered Batfamily but he has vanished so who knows.
then there are those who are close allies or affiliated but (at least for me) wouldn't be considered Batfamily:
Ghost-Maker
Clownhunter/Bao Pham
Harley Quinn
any non-Gothamite on The Outsiders
Grifter
Jim Gordan
Leslie Thompkins
Julia Pennyworth
Man-Bat
Clayface
then finally we have people who were part of the Batfamily but have fallen off:
Bette Kane/Firehawk
Kathy Kane/Batwoman
David Zavimbe/OG Batwing
Orpheus