No we don't lol
Haitians speak creole and those who don't, speak french, while dominicans speak only spanish. We don't even share words or slang in common. Haiti is almost like an alien culture right next to us.
Cuba, DR and PR are the ones who share the same history, language and culture. Also, the three nations (Cuba, DR, PR) are genetically interrelated, and to some extent Venezuela and the north coast of Colombia. For example, im 100% dominican, but i have distant relatives in Venezuela on my fathers side and PR on my mothers side, no relatives from Haiti. Simon Bolivar, the liberator of Venezuela, Colombia and Ecuador had dominican ancestors.
Its almost like 3 provinces of the same country, but with different political systems. There's more similarities between cubans and dominicans, than between two different regions of Colombia, just to put an example.
I know this goes against the Coli narrative, that dominicans and haitians are brothers, etc. But the truth is, dominicans share very little with Haiti, both culturally and language wise. Genetically, the only people who are of haitian descent are those who grew up in "bateyes" and or were born in DR from haitian inmigrant parents.
By the way, when i talk about cubans, don't think about the Miami cubans. They're not at all representative of the real cubans from the island.