Ironically the more stable a metal is atomically the lower it's melting point. Larger (atomically larger) metals that ionize easily (meaning electrical conductors) tend to have high melting points. This seems like something I used to know the why of but I believe that brain cell that held that data was killed by bourbon.
Can't imagine you'd need to know the details for any practical applications, but chemically speaking that's all incorrect I'm afraid. I suspect you've misremembered some of the stuff on ductility/ malleability. There aren't really any rules for stability vs melting point, but there are some guidelines for other relationships like ability to make good wires and ability to conduct well being linked to having a medium MP (that the three best conductors in silver, gold and copper all make good wires and have MPs around 1000C is not coincidental).
I seem to remember that melting point and cohesion in general was a result of delocalized electrons. The amount of those depends on how many electrons there are in the highest energy orbitals compared to how many the orbital can hold (as in the case of mercury, both the d and s orbitals are full, so you have crap cohesion and a metal that is liquid at room temp). So, similar melting points within a group given their equivalent outer shell electronic configurations (as is the case with Cu, Ag and Au), increasing mp as period increases, and decreasing mp as we move to the right on the periodic table as orbitals get filled up.
Electronic configuration isn't as far as I know related to nucleus stability.
However that's all off the top of my head, and I'm getting stupider all the time, so it's entirely possible that all of the above is complete nonsense.