trip from puerto plata to samana

Take the airport access road to the highway. Turn left. Stay on that road to Nagua and continue until you see a sign for road to Samana. You don't want to go west from Nagua to San Francisco de Macoris, go east to Samana. About an hour after you leave Nagua, you will come to Sanchez. The highway passes on the outskirts. Continue until you get past Sanchez and see what looks like a major highway on your left. You should also see a sign. There is a big fereteria (hardware store) on one corner. Turn left and take that road over the mountains to La Terrerenas. Drive carefully; road is good but there are mountain curves. This is a very scenic route. Or you can pass that turn and continue for about another 20 minutes until you are approaching outskirts of Samana. There is another good road there to Las Terrenas. Less scenic but less curves. Have a good trip. Your trip is going to take you about 4 hours.

I don't know what the car rental charge is, but I'd suggest seriously considering taking a taxi. It will cost about RD$1500, but it will be easier on you and probably faster. If there are several in your party, this won't increase the price. The charge is for the taxi.

Another option is to charter a small plane at POP airport to take you to the small airport in Las Terrenas.

Car rental is expensive and if you don't plan to be using it every day, I think you would be better off to take a taxi and rent a car just for the periods that you need it.

Have you checked with your hotel to see if it would send a van-type taxi for you? There was another person recently with questions like yours (no dog, though) going to Las Terrenas. He ended up with a taxi sent to the airport by the hotel. He posted a report saying the driver spoke English, was knowledeable about the area, and gave him a wonderful tour on the drive to Las Terrenas. The charge for the taxi will be about the same, whether you take a taxi from airport or a taxi sent by the hotel. Both would have to make the same roundtrip. If I were you, I'd first contact your hotel and ask them for help.

If you take a taxi from airport and vehicles there aren't large enough to comfortably accomodate you and your dog all the way to Las Terrenas, take a taxi from airport to taxi stand in Sosua. There are a lot of van-type taxis there.