So the WH sets up the rules for press briefings: you get one and only one question and then you sit down. And you don't get to offer your sermon or analysis of the President's decisions or policies, you are there to get information and disseminate it to your audience. If you don't have the mike you cannot speak, and you are not allowed to interrupt the WH briefer once your question has been asked. Then set up the due process: both you and your media boss gets written notification of your failure to abide by the rules. Either you and/or your boss gets to appeal and make your case. Subsequent misbehavior will get your individual press pass suspended for say a week, then a month, then a year.
Seems to me the WH press briefings need not take questions; if members of the media cannot act in a respectful manner then the President or the Press Secretary can stop the briefing in progress at their discretion. Or walk in and give their briefing and then leave without taking questions, at least for awhile. An orderly and respectful briefing should be required, but the President can get his information out in a number of other ways. He can even accept written questions from the press or from the public, and provide responses on a WH website. IOW: no more political grandstanding bullshit.