Good question Dan, to really understand the answer you will have to consider the immense velocity that electrons travel at (nearly the speed of light - if we use theoretical models and instantaneous speeds);even thoght there may be a vast amount of space between the nucleus of the rock atom (which is debatable within itself), the electrons on the outer shell of atoms on our skin, are repelled by the fast moving electrons on the outer shell of a 'rock' atom.
As you have correctly mentioned, the strong nuclear force binds the protons and neutrons together as the electromagnetic force binds the protons and the electrons as they have opposite charges. Due to this force, the electrons in the outer shell of the rock repel the electrons on the outer shell of our skin which means that they are not totally separated.
So, in conclusion, what you 'feel' when you touch a rock is the repulsion of electrons and not any actual nuclei.
