Forget Punta Cana and fly into Santo Domingo.
One good possibility is to take a taxi from the airport to the Caribe Tours bus terminal. I think past posts in other threads have said this costs about US$25 dollars for the taxi. But tickets on the Caribe Tours bus to Sosua. This will cost you RD$240 or about US$8 per person. When you get to Sosua, take a taxi to your hotel in Cabarete. This will cost you about US$8 for the taxi.
Caribe Tour has buses leaving every hour from 6 or 7 am until 7 pm. The ride to Sosua will take about 4.5 hours, the cab to your hotel in Cabareta about 15 minutes.
Or take a taxi all the way. If you take a cab from the airport to your hotel, it it going to cost you more than US$100. You will have no trouble getting a taxi at the airport to take you all the way. If your family and luggage can fit comfortably in a taxi, it could be a good way to go and will get you to Cabarete faster than will a bus.
If you want to go to Cabarete, the idea about going to Punta Cana and taking a boat to Samana (after a long bus ride to get to the boat) makes no sense.