One must be careful in claiming that atoms are mostly empty space. That is just one point of view. Electrons and quarks behave like solid points whenever one attempts to measure their dimensions as particles, and from that point of view there certainly seems to be a great deal more space than matter within an atom, but in fact there are complications. Seen from another point of view, elementary particles have wave aspects and do occupy space, by which we mean that their presence is relevant. One example of such relevance is that no two particles with identical quantum numbers can occupy the same orbital, and we find that a full orbital accommodates two electrons only if their spins differ. Now, an orbital occupies a large space in atomic terms, so if we bring two atoms closer together till their orbitals begin to overlap, they will repel each other with great force. This is not what we would expect from simple "empty space". It is rather more like the behaviour of solids, and in fact atoms will rebound from atoms for both these and other reasons, such as the repulsion of the like charges of electrons.

There are contrary effects as well, or of course atoms would never stick to each other, and we know that in fact they do, both in simple adhesion and in chemical reaction. This happens when there are vacancies or ambiguities in the orbitals that a particular electron might be occupying, or partly occupying.

As for the atoms from separate objects "mingling" when they make contact, that depends. Certain atoms in particular states strongly repel each other, so that the objects they belong to hardly exchange atoms at all. In contrast, if you place two clean pieces of gold in contact, their atoms certainly can mingle, which is in fact what makes it possible for us to beat multiple pieces of gold into a single sheet. Less obviously if we place a very clean block of gold in close contact to a very clean block of silver, some of the atoms of each metal will diffuse into the opposite block.

It all depends on the nature of the materials and the nature of their contact.

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.