I don't see that you've offered a better alternative to VNM utility.

Your examples assert that VNM does a bad job of capturing subtleties in the structure of human preference. But they can all be fixed by using the appropriate outcome-space as your utility function's domain.

For example, if I prefer to decide which child gets a car with a fair coin flip, then I can represent my utility function like this:

U(son gets car after coin flip) = 10.1 U(daughter gets car after coin flip) = 10.1 U(son gets car after my arbitrary decision) = 10 U(daughter gets car after my arbitrary decision) = 10

To me this seems like an elegant enough way to capture my value of fairness. And this kind of VNM formulation is so precise that I think it is useful for defining exactly how I value fairness.

I think the alternate utility theories introduce complexity without improving decision theory.