The running theme in the episode is the "brand" mentality adopted not only by
The Prince and His Wife, but also by those onlookers to their shenanigans - in this case, Kyle. He realised he was losing his friends with his obsession. And that "branding" essentially limits you, such that you take your brand to stupid extremes, until people completely switch off from you. And then you have to rebrand again to get attention. The more you rebrand, the more you become an empty vessel (hence The Prince looking to see what was inside the Wife, who had been rebranded many times, and realising there was nothing inside). In contrast just being yourself and having real friends and real interactions is a winning formula, because you can't emulate what is genuine. Kyle learned the lesson that he could be annoyed with the Prince without having to completely change who he is, lose his rational mind and become a victim. The Prince learned that he didn't need to brand himself to get privacy, he just had to live the life he was asking for and get on with being himself. It's such clever writing.
The looking down The Wife's throat thing is a visual metaphor for looking inside someone to see if they have any substance and soul. It is not a depiction of decapitation or any other sort of violence. But the fact that it has been stated to be such proves the writers' point about branding most admirably. If your brand is to interpret everything said or done as a potential act of aggression towards a person or group of people, then the natural end point is completely misinterpreting a cartoon that has run for 26 years - throughout which Canadians are portrayed as having a hinged mouth (in order to differentiate them from Americans) - and saying it depicts a violent image when that cartoon Canadian is a black princess.