You have it down pat regarding weather in the DR and the Caribbean. What you describe is most likely what you will find in November. Actually November is a great time to travel, because you avoid the two hot months of the year, which are the summer months, when temperatures can go up to 33-34C. But again, the DR, and Punta Cana is blessed by winds blowing from the sea that don't let it get as hot, even in summer, as Rome or New York, for example.
As weather has changed, it is more volatile and it is hard to tell when the rainy season of the year is anymore. Reality is that any time of the year, you could run into a raining spat of three-four days of straight rain, but that is the exception, not the norm, usually caused by a tropical wave or tropical storm in the area. And these are even rarer in areas like Punta Cana, Juan Dolio or Barahona in the southwest. So, your chances for good weather are very good.
Here at DR we empower you with all sorts of links to follow the weather. See the Current Weather links at
http://dr1.com/weather/hurricanes.shtml#3 to follow the satellite picture as the time of your arrival gets closer. You can also check in with this section, as your arrival date comes closer. We frequently post updates that are eyewitness reports, from people that are actually there.
And once in Punta Cana, please post the weather from there for readers to get a better grasp of weather in the area.