^So Imam ZainulAbidin and Imam Jafar Sadiq are not Ahle-bait, agreed!
it boils down to infallibility and in whose progeny imamate was subsequently transfered as believed by 12ers
many hussanid imams are not "imams" per 12ers
none of the hassanid imams are "imams"
and other sons of Ali never ever in the counting.
progeny of abbass got booted out of ahlulbayt when differneces between shia factions flared after the revolution against ummayyads.( although it has be said very few abbassid were worthy of it )