So there are two thoughts here depending on your goal.
One: The understanding of the nature of the universe:
“All motion” is not relative. Relativity only holds for something called “inertial frames” which is a fancy way of saying that your reference need to obey Newtons first law: Objects at rest stay at rest, and objects moving will move in a straight line, unless acted on by another force.
In the simplest (ELI5) terms: velocity is relative but acceleration is not.
Something “Rotating around us in a right weird and [non-]uniform way” would require objects to be under weird and non-uniform acceleration. Since acceleration is not relative, we could detect that acceleration if it existed.
Two: The “usefulness” of a theory as a model. The current theory lets us correctly predict a lot of useful things. As far as I can tell the “weird and non-uniform way” motion would allow us to predict less. So the value of the current theory as a model would be higher than the value of the new theory as a model.
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