The Dominican Republic is one of the best destinations in the Caribbean for road trips. The reason is that the roads here are good and there is lots to see and do.
If you are interested in cigars, the two options are Santiago and La Romana (in the southeast).
There is a well run cigar operation in La Romana:
Cigar Country Tours - Tours & Excursions - La Romana, Dominican Republic.
See
http://dr1.com/travel/laromanaguide.pdf for suggestions of what there is to do.
Staying in La Romana you have Bayahibe/Dominicus beach + you can take the children to the new Los Delfines Water Park (midway between Boca Chica and Juan Dolio). You could consider one of the resorts in Dominicus, or one of the small hotels in Bayahibe. Check out
Hotels & Resorts - Directories, Dominican Republic.
In Santo Domingo there are many parks for the children, including several at shopping malls. For instance, there is an aquarium that has just opened at Sambil Mall with a very good showing of marine creatures. The children will especially enjoy it. 360 Galerias (Americana Departamentos), Agora Mall, Silversun all have good sized entertainment parks for the children. There is also the National Zoo that has the lemur monkeys. That zoo has a good children's petting section, and it is a lovely nature walk.
Samana works well with a 7 day trip, but I would stay at different hotels making my way to Samana city, Las Galeras and then Las Terrenas. But you would be too far from Santiago -- 3 hours drive.
http://dr1.com/travel/samanaguide.pdf
The Santo Domingo guide -- sending here the Spanish version -- is an older one. The new one will be out later this month.
http://dr1.com/travel/santodomingoguideEspanol.pdf
But it helps give you an idea of what to do in the capital city.
From La Romana, you can be in the city in two hours.
If you decide to head north, the children will have a great time at the Ocean World Park.
Ocean World Adventure Park - Tours & Excursions - Puerto Plata, Dominican Republic.
For a family with two small children, driving all the way out to La Isabela is too much. And I would leave Damajagua for when the children are older. Cabarete is famous for its water sports, that your children will not very much be into now -- windsurfing and kiteboarding or surfing. But the beach is fine for swimming close to shore.
So my recommendation is this time around to choose La Romana.