[danbruc]

The interactions inside atoms seem to have no known relations to EM [...]

The electromagnetic and the weak interaction are known to be different aspects of the unified electroweak interaction. There are several grand unified theories and a few hints that at even higher energies the electroweak and strong interaction also unifiy into the electronuclear interaction. Due to the high energies involved, only indirect experimental evidence seems accessable for the forseeable future but there are various groups looking for hints. I am not aware of any uncontroversial results but there are a few non-reproducable experiments, for example observations of magnetic monopoles, which might be due to experimental error but also due to the rarity of magnetic monopoles.