Your invocation of determinism is a red herring. There is no scientifically testable formulation of the philosophical problem of free will vs determinism. It isn't an issue in science because it can't be described in a way that can be falsified. It is beside the point in a deeper way. The problem of constancy in natural laws would not be changed by either side of the philosophical problem. If everything is determined, it is of no practical consequence, because quantum indeterminancy, chaos and complexity pose an infinite horizon for our ability to predict. We can never achieve the detailed knowledge needed to see the future, even if it is completely determined.
On the other hand, free will does not grant us the ability to change physical laws.