“If the nucleus of an atom is essentially a positive charge and the circling electrons are negative .... only the finger of GOD keeps the thing from imploding”
Well, positive and negative electrical charges do not obliterate each other, like matter and antimatter do. They simply strive to achieve equilibrium of charges, which you have in a stable atom. What keeps them from continuing to attract each other until the particles actually collide is probably just the kinetic energy of the electrons. They can’t slow down to come into contact with the nucleus, so the closest they can achieve is a close, stable orbit.
OK ... GOD keeps the dervishes whirling
But electrons don't, and so we have quantum mechanics, i.e. have a set of mathematical equations that predict exactly what electrons will do, in some case exactly and in other cases probabilistically, but we still don't really know why the electron doesn't collapse into the nucleus.
The QM explanation is that electrons can only lose quantized amounts of energy, i.e. they can't just slowly run down. So the electron stays in orbit until something happens such that it can gain a quanta of energy and get thrown out of orbit, or into a higher orbit, or lose a quanta of energy and go into a lower orbit.
Of course in QM electrons don't necessarily exist at one point in space and so don't really orbit nuclei in the same way that planets orbit the sun.
So, yes we have the math to predict what will happen, but we still have no idea why what happens actually does.