What 'special status' are you talking about?
She's currently sole trustee of the trust that owns the Clippers, but that trust will lose ownership completely upon completion of the sale. She will have no 'status' with regard to the Clippers at that point.
And, no, people can get banned from attending NBA games. Just because they sell tickets to the public doesn't make it a 'public event'. It happens within an arena as a business venture and businesses have the right to refuse sale of tickets to individuals.
People get tossed out and sometimes banned from sporting arenas all the time. I remember some dude running out onto Camden Yards in a batman costume a few years ago got banned for life.
I suspect that such bans are not really, for all practical purposes, enforceable for the typical jerk who got kicked out for some unruly behavior. Those sorts of guys probably just walk right in again without being recognized.
But Sterling is a pretty recognizable figure and would almost certainly be flagged by someone if he showed up in an NBA arena.
I'm not really seeing how things ended up in 'the middle'. Sterling is still banned for life and the team is being sold.