If Jupiter and Saturn were considered stars, which of their moons would qualify as planets by 'clearing the neighbourhood'? Jupiter has four and Saturn seven spherical satellites. Jupiter's moon Ganymede and Saturn's Titan are larger than Mercury and they're the most massive moons at 0.0248 M♁ (Ganymede) and 0.0225 M♁ (Titan). Do these moons 'shepherd' the other moons' and asteroidal satellites' orbits? Ganymede is three times the mass of Europa and quite close to it, so does it dominate Europa's orbit? Callisto on the other hand is twice as far as Ganymede and the 3rd most large and massive known moon while quite lonely in its orbit. Would it qualify for a planet too? If Jupiter was a star, I think Ganymede and Callisto would qualify as planets, Europa would be a 'dwarf planet' (because of being dominated by Ganymede's and perhaps Io's orbit) and Io I don't know, it probably would be more controversial.
Saturn's moon Titan is more massive than the other six spherical moons altogether, so I think it would clearly be a planet. The other moons (except Iapetus) are quite close to each other so I think they'd be considered 'dwarf planets' except Iapetus which is very far from Saturn and also quite lonely, so it might qualify as a planet (there might be an issue concerning its shape but my question is about the 'clearing the neighbourhood'/planetary discriminant point). Mimas would near-certainly be a 'dwarf planet' because it's about within the rings which alone are about 2/5 the mass of Mimas. So I think Titan and Iapetus would be considered 'planets', Mimas a 'dwarf planet' and the other spherical moons of Saturn probably too.
What would you say? Which Jovian and Saturnian moons would be considered planets and which ones 'dwarf planets' as per the proposed planetary discriminants if Jupiter and Saturn were stars?
I've noted before that the IAU naming critera are guidelines rather than laws of nature.  If applied to Jupiter's moons the four Galilean satellites would probably be &quot;planets&quot; (they don't share their orbits with anything else of comparable size and are large enought to be in hydrostatic equilibrium)  There is a mean-motion resonance 4:2:1 between them but this is a more or less symmetric relationship without one body dominating another.
The other moons are tiny by comparison.  There are 4 major bodies orbiting Jupiter.
For Saturn, Titan certainly dominates its orbit (Hyperion is much smaller.)  Dione and Rhea also seem to have a value of mu that are over 100 (though determining the value is tricky because not all moons and moonlets have been discovered) Enceladus and Tethys and Iapetus also seem to qualify,  As you note, Mimas is too small and borderline spherical. The other moons are just so much shrapnel by comparison.
So there would probably be the six pre-1800 moons, minus Mimas.
It is possible that the rules might be bent, the Rings are no permanent features, so they might be ignored for the sake of planetary determination. Remember the rules exist to serve us.  Humans make the rules. Some can be bent, some broken.