driving from kingston to port antonio takes about 2 hours.
driving from mobay takes about 4 hours.
i personally would fly into kingston and hire a driver or take knutsford express to port antonio.
then same thing from port antonio to negril (hire a driver or take the bus).
then fly out of montego bay.
12 days is definitely enough to do both places, but you also might want to consider breaking up the 6 hour drive from port antonio to negril. i remember we stayed the night in ochi the one time i drove from negril to port antonio.