When we got our basement finished, we wanted to isolate teenager noise to the upper floor, so we did the insulation and resilient channels. Works very well for regular noise transfer between floors (only deep bass is heard at all, really). Can't comment much on hardwood floor noise, however, as the busy area on the top floor is carpeted. No one at home to test with me right now, but my recollection would be that footfall on hardwood sections is still quite audible, but very muffled and not annoying. I supposed if I can't really remember then it must not be very noticeable.
I also remember seeing something about two layers of drywall in an episode of Income Property. Searching a bit on that, I found a nice link (
http://www.soundproofingcompany.com/soundproofing-solutions/soundproof-a-ceiling/) where the better solutions use two layers with a "green glue" layer in between.
I suggest you make sure whatever you do meets fire code for an accessory apartment and get it inspected. I believe it comes down mainly to the drywall being thick enough (or of special fire rating type), which should be compatible or very close to the sound-proofing strategies.
Another requirement for legal accessory apartments is minimum heights -- hopefully your is high enough, but if borderline then your ceiling strategy might need to be adapted if you want to stay within those requirements.