If the decision was made outside the confines of a proper meeting – ie, there was no notice of the meeting, no agenda and no minutes of the meeting any orders purporting to be from the EC would almost certainly be thrown out. EC's have a certain amount of leeway to help with the day-to-day running of their buildings but when it comes to issues of breaches of by-laws, the CTTT tends to insist that the letter of the law is followed if for no other reason than owners need to know action is being taken against them and have a chance to defend themselves at the meeting.
On the question of getting rid of them, the easiest way is to either reduce the size of the EC at the next meeting and them make sure you have the numbers to get your people elected or stand allternative candidates as a “ticket” (again assuming you have the numbers).
But be careful not to let your campaigning get out of hand. Thers is only limited “privilege' in Executive Committee communications and if your criticisms can be shown to be defamatory and, even worse, malicious you could be sued (I mention this because exactly that has happened to my partner).