<b>[Stoat] "This thing would be essentially a part of the core ... "</b>
In a true central explosion of a 4 to 5 Earth-mass (or larger) planet, essentially 100% of the planet is vaporized. The 4 to 5 Earth-mass constraint is of course theory (model) dependent. For smaller planets, as the mass drops below the divding line and some mass is not vaporized, the crust is the part that survives.
<b>[Stoat] "I still haven't worked out the time this explosion took."</b>
That wil be hard to do with any certainty. There are a lot of factors that can influence this and until we see a few of these things happen in person we can only come up with a range of possibilities.
<b>[Stoat] " ... inner moons would fly off into solar orbits once the bulk of the exploding planet was outside their orbits. This would be at different times."</b>
An explosion of this size is a process, not an event. Your intuition is working well. Even so, the process will run its course in a matter of hours. The less energetic the explosion the longer it will take, but if the available energy is too low the explosion will fizzle.
<ul>Some internal material might be vaproized and escape. Some crustal material might be propelled into space, mostly with less than escape velocity. The planet will be destroyed, but it will not explode in the way we normally imagine. It will continue to move as a single mass in its usual orbit.</ul>
Suppose it takes 15 hours from start (first burp) to finish (trailing edge of blast wave sweeps past a moon with a million kilometer orbit). The moons will be almost in the same place, moving with almost the same velocity, the whole time. Very close asteroidal moons might be an exception.
But whether the explosion takes a year or a microsecond (or half a moon's orbital period versus a tiny fraction of that period), the directions of travel of the moon or moons will be random and their speeds will be what they are prior to the explosion.
LB
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