It is possible, on a good day with every connection perfect to make it in 7 hours on two buses. You are better off flying into PUJ, LRM or SDQ, as I am sure you figured out too late!
right Ian,
and those 7hrs would be record time quick, ha ha.
check local flights from Puerto Plata to PuJ and back to PoP afterwards,
on the road you would waste minimum 2 vacation days for that Inland travel, most likely 3 depending on the Time the flight back home leaves Puerto Plata, no Night Bus available, so on the way back home to catch the flight in Puerto Plata you may need to catch a Bus the prior Day and spend a night in PoP.
Mike