Albus didn't divulge that the barman of the Hog's Head was Aberforth, but he didn't deny it either.
We do know Aberforth was in the Order of the Phoenix so they must have had a later cordial relationship, and Moody at least knew he was Dumbledore's brother.
The little people in the photograph jostled among themselves and those hidden right at the back appeared at the forefront of the picture. ‘That’s Dumbledore’s brother Aberforth, only time I ever met him, strange bloke … that’s Dorcas Meadowes, Voldemort killed her personally … Sirius, when he still had short hair … and … there you go, thought that would interest you!’
Harry Potter and The Order of the Phoenix | Chapter 9: The Woes of Mrs Weasley
He also never hid the fact he had a sister, he just wasn't asked.
Harry, in Harry Potter and the Deathly Hallows, comes to the realisation that in all his meetings with Dumbledore he never once asked him about himself and his family, and as we only see Dumbledore through the eyes of the Harry we don't get to learn his past.
Aberforth blamed Albus for the death of their sister. That's why they fell out.