No way you can gat there in 3 hours.
Santiago to Capital very quick driving - 1 hour (that is what I can do going 140/150/160 wherever possible)
30 minutes to cross capital with no traffic - M Gomez & 27
2 hours to Higuey with no traffic - from M Gomez & 27
45 minutes to Bavaro/ Punta Cana with no traffic - watch for huge potholes that can send your whole tren lantero to a junkyard
so it's a bit over 4 hours, reckless driving, with no traffic
now a comfortable driving, AND considering traffic, and not driving like you are in a car chase:
Santiago to Capital - 1 hour 20 minutes
Capital - 40 minutes
to Higuey 2 hours 20 minutes
to Bavaro 1 hour
total: 5 hour 20 minutes.