I think it's a cool POD, but IMHO it'd end up like Puerto Rico, as a Commonwealth, and for all the same reasons. Notice the culture and geography aren't so different. I recommend reading up on some PR history.
There would be little assimilation because of US racism and colonialism, which sought to "protect" the poor natives from themselves, including by locals being treated racistly by American banks and other businesses, and taking all the power for unelected commisisioners who stole everything in sight and didn't care enough about "the natives" to look around or understand much. PR poverty and life expectancy stayed miserable until the Commonwealth was started and Puerto Ricans allowed to elect ALL local officials. Unlike DC, they don't face federal taxation without Congressional representation.
Do notice, there were no boatloads of blacks to PR, and it'd be the same for an American Dominican Republic. As in the US, social place in most of Latin America, especially before antiracism efforts, was well-correlated with skin color, and for exactly the same reason.
And, Pervez, before we get too idealistic about the US in the Caribbean before we gave up on imperialism, how happy was Columbia to give up Panama, and Cuba to sign the long-term Gitmo lease?