One possible solution would be for each NBA and NFL to be required to maintain its own maximum security prison facility for its ‘thug’ players. League Rules could be adopted which require every team to keep its 'thug' players locked up in the team prison, except during practices and games.
Any player (or coach) which the team hires or drafts who has a violent criminal record, or who is arrested for a violent crime while working for the team would be classified as a 'thug'.
Away games could be handled by further requiring that every team in the league maintain 'guest cells' in its team prison so that visiting 'thug' players could be kept under lock and key when not playing or practicing – (this is not really very different from the guest locker rooms which teams are required to maintain in their stadiums).
It would require that each team add a concrete block building to its stadium and/or practice facilities, hire trained prison guards, buy a team bus with bars on the windows and possibly surround its practice facilities and playing field with razor-wire.
I’m sure there would be other security-related expenses, but most, if not all, of these added expenses would be off-set by savings in team legal expenses and in the cost savings realized by NOT having to regularly hold press conferences to make statements about how 'disappointed' the team/coach/owner is in the behavior of the latest and greatest ‘thug’ they have agreed to pay millions of dollars a year to play a game for a living.
I like you idea! You would think that as much money that these teams have invested in a player that they could hire 24 hour babysitters for them. It would probably be worth the money to keep their top players out of trouble.