You are combining a bunch of different and only loosely related issues here. In no particular order:
- If you plan on starting anywhere except with the status quo, you're wasting your time. It is impossible to sensibly criticize, let alone improve on, a theory until know what the theory says.
- A. Neumaier's reply above is a pretty good summary of the accepted status of determinism in modern science. If you want to know more about how we arrived here and the strengths and limitations of that worldview, you have more than two centuries of catching up to do: Start with "Laplace's Demon".
- Hidden variable theories are far from being "one of the main problems in quantum physics today", and in any case are only loosely related to determinism; there's no reason why a hidden variable theory has to be deterministic. It is true that Einstein and colleagues wrote a paper on the incompleteness of quantum mechanics 80 years ago, and it is true that a deterministic hidden variable theory would go a long ways towards addressing their criticisms - but subsequent theoretical and experimental developments have shown that a theory of the type they imagined is not possible.
Although there is no substitute for really learning the physics, you may find several books helpful. These are layman-friendly, and not a substitute for the real thing... but they also do not require a fair amount of math background and several months of concentrated effort to get through:
- Giancarlo Ghiardi: Sneaking a look at God's cards
- Louisa Golder: The age of entanglement
- David Lindley: Where does the wierdness go?