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?
Absolutely. I think you bring up great points and it's an interesting discussion to have. I agree 100% that just having nuclear weapons doesn't automatically grant perfect sovereignty. Nothing does that. I'm only saying that puppet states don't develop their own nuclear weapons.
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.
Yes, basically this. And of course the power balance there skews towards the US (how could it not).