Cannot comment on the road block part, as I have never seen one (driven years between the two places), so I'd assume they don't happen very often, unless there is a huelga.
From Santo Domingo, you take the Autopista Duarte (nro 1), entering to Santiago, you can bypass the city via the Circunvalacion Norte (highway with 4 lanes also), then continue back with Autopista Joaquin Balaguer (also the nro 1) up until Navarrete, from where you have to turn right, and the rest of the trip to Puerto Plata is a two-lane street which is currently not in a very good shape... I've seen others mentioning other routes from Santiago to Puerto Plata, but won't comment on those as I've never used them, but always the Navarrete-Puerto Plata route.
I've driven countless times even at midnight, and while it's definitely not that fun, in my opinion, if you have no other options, it's feasible. The only part that I currently really dislike is exactly that two-lane road between Navarrete and Puerto Plata, which has partly unusable markings, part of the road is destroyed due to weather or construction, part of the asphalt is also missing and there are quite a few potholes, so unless you know the street well, I would hesitate taking that part in dark. I've done it, and nothing bad happened, but I did not really enjoy that...