Like dmckee says, the potential energy of electrons in an atom doesn't really compare to the energy of the nucleus. Since the nucleus is so tightly packed, and (in the case of Uranium) contains so many protons, they have a lot of potential energy—it takes a lot of work to "push" them together. The strong force holds protons and neutrons together when they're close enough together. It's sometimes compared to a glue in that sense. However, this force disappears very quickly once the nucleons become separated past a certain distance (on the order of a femtometer), so for a large nucleus like that of Uranium, the protons on one end of the nucleus aren't "stuck" to the protons on the other side, but there's still plenty of electrostatic force pushing them apart. That's why large nuclei are unstable; especially those with a higher proton-to-neutron ratio, like U-235 (or U-236). If you can destabilize that nucleus enough (you could imagine it stretching out like a football), its own electric force will tear it apart, and release a tremendous amount of energy as the fragments accelerate apart.
It seems that you've already considered that to a degree, but yes, you don't have to worry about electrons. Just think about the protons, because the nucleus is definitely not neutral. It is a bit of a problem if you don't know how close together those nuclear fragments start out, but you could probably estimate it by considering the nuclear radius of uranium, which is about 7 or 8 fm (it's hard to find an exact figure), or by using double the radius of the fragments it creates, which, it would seem, would be paladium nuclei. Obviously the protons weren't in the same place when they start out, but they were very close together.