Why does the shithole country Haiti, which shares the same island with the relatively stable and semi-prosperous Dominican Republic, have such massive problems?

They have similar demographics, and pre-colonial backgrounds. Ah, it was the Haitian slave revolt you say? Yes, but only partially. The country was dedicated to Satan at its revolt, and renews its pact every year when they celebrate their independence.

On August 14, 1791, the one who led the first plantation revolt, Boukman, uttered these words quoted in The Black Jacobins: “The god who created the sun which gives us light, who rouses the waves and rules the storm, though hidden in the clouds, he watches us. He sees all that the white man does. The god of the white man inspires us with crime, but our god calls upon us to do good works. Our god who is good to us orders us to revenge our wrongs. He will direct our arms and aid us. Throw away the symbol of the god of the whites who has caused us to weep, and listen to the voices of liberty, which speaks in the hearts of us all.”

Six days later the plantation slaves, led by Boukman, indiscriminately massacred every white man, woman, and child they could find. This action was the start of the ultimately successful slave revolt, though it went on for 12 years before it ended.

The rampant practice of voodoo doesn't help the underdevelopment, government corruption, endemic poverty, earthquakes, violence, and cannibalism.