Of course, the people would fight against the US invasion, but how much of the population would be willing to die to get the Anglos off of their island? The standing US Army was ridiculously small at the time (I think it had like 30,000 soldiers), but it would be operating in a very small area with a low population.
Also, the US proved it was willing to throw tons of soldiers away to occupy colonial territory, even when there were better options. More than 100,000 US soldiers were sent to the Philippines IOTL, even though the US could have gotten the same strategic position in the Pacific by just taking Luzon instead of the whole territory.
If that same force was sent to the Dominican Republic, it's hard to see how an occupation would fail. I'm sure that the Dominicans would be extremely resistant to US annexation, but the same could be said for the people of Puerto Rico IOTL, and look how that turned out.
Edit: And just to give a clearer picture of what 100,000 US troops occupying the Dominican Republic would be like, it's the same thing (proportionally) as occupying Belgium with 3 million soldiers, or the Philippines with 30 million.