Another possibility would be for the ruler to simply terminate the interview, have the visiting delegation escorted out, and tell them they can return when they learn how to conduct themselves.
What do you need the scene for? What are you trying to achieve? Your question sounds like it's something that just happened independently of you and now you have to deal with it somehow. In reality, it's a scene you are creating. So what's its purpose? The point is, you can choose how the ruler reacts depending on in which direction you want your story to head from there.
I'd say it'd largely depend on the era and region. An american president would likely react differently than King Edward the First for example. It also largely depends on the culture, and as others said what you're attempting to accomplish with the scene.
Allow me to offer a real-world example. Prince Vlad III received 3 "ambassadors" from the Ottoman Empire. sometime in the mid 15th century. They refused to doff their turbans claiming they only do for that for their Emperor. Vlad ordered the turbans be nailed to their heads and expelled them. Wallachia and the Ottoman Empire were already in a hostile situation, so it didn't really deteriorate relations.
"Off with their heads!" is the command of someone who lets others do the work. If they lead from the front, perhaps they'd take action themselves:
Assault by proxy. The She who is the villain using her pawns to inflict damage and/or insult. No matter how the King reacts, she wins in some small way. The best he can do, if he doesn't have a violent temper, would be to try to mitigate the damage to his reputation while not also damaging his relations to the proxies with a too violent response. Cause you know those proxies will spin the altercation when they get home with an explanation that puts them in a good light, esp among their own people. Win/Win for She. Although... Perhaps, after the first or second interruption he rises from the throne and advances as he speaks. Another interruption and a hand signal starts to draw in the royal guard who begin advancing with him. So each time there is an interruption, he gets and closer, and so do the armed guards who are looking more threatening with each step they take. Pretty soon, they are going to be ringed in, and all without the King becoming verbally threatening. If they want to be martyrs they can keep talking. On their heads be it...
I have a similar situation where the Tyrant is compelled to decide, only it's a vest bomber. He is the one presenting himself before the King to challenge for his kingdom by right of ritual combat. It is something the King and many others desperately wanted to happen to prevent carnage. The bomb attempt is exactly what it looks like, a cowardly and juvenile act of selfish desperation. They are both challenged with making a critical no-win decision in an instant. The Tyrant decides to pull his ace, a secret weapon that should not be exposed, just as an unexpected power intervenes. It is locally more powerful than the Tyrant's globally powerful weapon - completely unexpected even by the King. The Tyrant shows his character in deciding to act without hesitation, to do what must be done knowing nothing else). The intervention is the opportunity for the King to demonstrate his noble wisdom by focusing on the greater priority, thus leaving the rash incident a mere inconvenience. The point is showing character and wisdom through action and non-action, making diplomacy more important than the risk of distraction. This also publicly renders the conspirators impotent. The purpose is also to introduce new characters and remind the reader of the potency of quiet ones. "It ain't speed that wins the race. It's how you take the curves." - anon
Unless this is something that has already planned, that being the Kings reaction to an unanticipated event, then I think a hand signal of some sort is needed. Either subtle or obvious, either works. The guard captain should be watching his King for signals, esp if he is being insulted. A little summoning gesture should get him moving and then the guards take the cues from him. And the royal guard should be in-tune with their King in order to respond even to his unspoken wishes.
Of course, you could also approach the situation as a culture clash. Some cultures have elaborate rituals for formal meetings. Those who do not follow the "rules of conduct" of such meetings are considered crass barbarians. Western cultures, especially the US, tend to be very direct. Asian cultures, Japan, for example, speak more subtly. During the Cold War a group of Soviet performers came to the US. The response was tumultuous and typically American, a standing ovation with applause, shouts and whistles. The Soviet performers were crushed, feeling that the performance had gone poorly. Why? In Russian culture (at the time) whistles were a sign of disapproval. In the current world of diplomacy, informality is the show of importance and respect, as the meeting is stripped of all its pomp and ceremony. It is standard practice to use translators, even if both parties can speak a common language; this way the translator can be said to have mis-spoken if the situation becomes tense. So perhaps misunderstanding each other is a place to start.
