Well, I was just thinking about how people are saying that it's reductive to say that one country strictly controls another, but at the same time it feels reductive to me to act like having nuclear weapons grants a country complete, supreme, perfect, and total sovereignty over itself. But you aren't saying that, anyways: you're saying that (intelligent actors within) both the Zionist entity and Seppoland can and do influence each other and can be pushed by the other to do things that go against their own interests, despite both polities being nuclear states.
Now your analysis of mutual influence to me seems absolutely correct, but I still think it raises the question of what the limits of nuclear weapons are when it comes to guaranteeing national sovereignty, and what the mechanisms of influence tend to be between two nuclear states. Because puppets or not, it still feels fair to say that the Zionist entity, UK, and France are all below Seppoland in the "pecking order", right? When painting in broad strokes, at least. So I figured it might be useful to compare and contrast these four polities' relationships to each other, basically. That this might be a way to land on a more holistic and accurate understanding of the dynamics at play.