Well, depends what you mean by 'core'. A Jovian core is radically different from a Terran core. Plus there's a big distinction in rocky worlds between an active geologic core and one that's 'switched off'. Therefore I don't think that's a good distinction for deciding what makes a 'planet'. (I mean I just point at the centre of any round astronomical object and it's got a core by definition - even our Moon's is actually still quite toasty, just that it doesn't do anything now
)
The reason I thought briefly that an atmosphere might be a valid, relatively simple requisite to define a major planet from a minor planet is because it is chiefly dependent on it's mass. A bit like the distinction between brown dwarfs and Jupiter-like objects: At about 14 Masses x Jupiter it is believed that a form of nuclear fusion would be initiated in the object. Below that it can't. That seems a nice physical cut-off that tells us something about the object.
So a more exact distinction that might make the cut-off for a planet is 'can this planet
sustain any sort of atmosphere at
all times?' The exact composition of the atmosphere will depend on a number of factors of course - but all the major planets have an atmosphere - Venus is CO2, Earth is NO2/O2 and the Gas/Ice giants largely Hydrogen/Helium. Thus Mercury is kicked out to become a minor planet...and Mars is close to the edge
.
Take the example you said. A Europan-type world with a giant moon skimming by it. If the Europan world was too small, it wouldn't matter in the long-term that the friction caused by the orbiting moon actually caused an atmosphere - it would be continually leaking gas into space all the time.
Magnetic field may be relevant it is useful at slowing the solar wind strip the atmosphere away. But the process of atmosphere stripping is, as far as I can see, continuous and will happen even for planets like us (I can't see an atmosphere being permanently charged forever as you mused, most big objects formed must be broadly electrically neutral, given that the universe is, we believe, electrically neutral. But hey, the universe is a big place, perhaps there is some way of doing that...) Again my thinking is that, if the mass is big enough, then the planet will have an atmosphere ('cause it starts with lots of it) so that it lasts for main sequence lifetime of the star it orbits. (Again Mars is very close to the edge
)
True temperature, or really, the distance the planet is from it's star will have a big impact on the
composition of the planet's atmosphere. Something the size of Earth orbiting at the same distance to Neptune will have gases such as Oxygen, Carbon dioxide and (quite a lot of its) Nitrogen frozen out, but actually at the temperatures present there, it would be easy to form and hold quite a dense atmosphere of Hydrogen and Helium.
Anyway I wasn't being too serious, as Vertigo says, this is about labels. Every object in the universe is interesting in it's own way.