For that to happen it requires Haiti to not invade, which would require a POD in which the French debt to Haiti is paid off or cancelled. Probably would require a POD in the 1790s-Napoleonic.
For one, its wasn't the Dominican Republic yet, it was Spanish Haiti.
No Haitian invasion of Dominican Republic has *huge* effects on the Dominican Republic, culturally. For better or for worse, the Dominican identity was formed in reaction to the Haitian invasion. There will be much less stigma against Haiti, Haitians, the French language and dark skin in general. On the other hand, slavery stays longer.
Economically this implies that Haiti has the debt paid off, allowing them to invest more in their country. The Dominican side of the island will be richer, as there is no mismanagement of the land during the Haitian occupation.
I don't know if Gran Colombia still breaks up, but assuming it doesn't, the entire region will be stronger. Trade with the Dominicans benefits both parties. Might also give incentive for Gran Colombia to invest in the navy and in the Caribbean in general.
Culturally, the two areas will be more similar. If this union lasts up until the present day, than the two cultures will be very intertwined, albeit each area will have its own unique culture. Although, the Dominicans will be more culturally distinct compared to others in the country. Expect to see more French and Haitian influence. Your average Dominican will be darker than your average Gran Colombian.
Linguistically expect Dominican Spanish to be potentially more similar to Venezuelan Spanish (Which they are pretty similar too in OTL, but even more). Colombian Spanish will probably be much more like its neighbors.
Probably, at which point Haiti invades anyway.
In all seriousness, that's my best guess for this one, but I could be wrong.
Possibly. Again, no Haitian invasion in the first place implies they have no reason to invade, which means either the Dominican side is stronger, or the Haitians are less desperate.
I could see if Gran Colombia breaks up as in OTL, Haiti invading again to capitalize on the opportunity