Laguna Lemon is excellent, instead of hotel la cueva, stay at Harley's heaven, just next door, I can get you the phone if you interested. If you would have 4x4 you could explore the beaches properly around there. But you will need at least beach chairs, as there is nothing there.
If you stay around Barahona, try to stay longer, the coast b/w Barahona and Oviedo is beautiful. check my pictures at
David's Pictures of Dominican Republic
I would strongly recommend to drive all the way to Bahia de las Aguilas (about 2.5 hr drive from Barahona, if you have no 4x4 you will need to take a boat from the park entrance, but it is most amazing place in DR.
I would give a skip to lago enriquillo, not much to see there. see my last post on the subject
Trip to Lago Enriquillo, Polo and Bahia de las Aguilas
The coast there is also very beautiful.
I am not sure that the coast around Puerto Plata - Cabarete - Sosua should get two days, depends on what you want, if you are after nightlife, then yes, if you want to see some natural beauty, you will be better of spending your time at Samana, Jarabacoa or SouthWest.
See my short post on this here (post 24):
Pictures from my trips
Jarabacoa has some nice places, especially the waterfalls, if you would have SUV I would recommend that you would drive from Jarabacaoa - Cosntanza - and through valle nuevo to San Jose de Ocoa and from there to Barahona. Even though this might be just about possible to drive with a ordinary car, you will hit lots of rocks and beat the hell out if it. Maybe not a trip for 3 year old, but definitely something you will not forget.
If you interested I can give you GPS or Google earth tracks.
Santo Domingo is in my opinion also worth only a passing visit, unless you are after some night life.
Once you work out your travel plan I can give you some places where I have stayed.
As to travel with kids, it might be lot of driving for a 3 year old, the main roads are generally ok, but you will have to watch for potholes even on a "freeway", that is the fact of life in DR. Be prepared that majority of Dominican drivers do not use indicators, mirrors, have no idea what the dividing line is for, and believe that they are the only ones using the road.