No, it was a miracle both periods lasted as long as they did.
The first period from 1801-1809 was not under Haitian rule- it was under French Rule. Under the treaty of Basel in 1795 Spain ceded Spanish Santo Domingo. The French Republic at the time reorganized it into 2 overseas departments legally and administratively distinct from the colony of Saint Domingue. When Toussaint marched in later he maintained the divisions and courted the Spanish inhabitants (as they had given him and his family shelter earlier on and he did fight in the Spanish army), de facto giving autonomy if not independence in every way sans foreign policy as the constitution of 1801 stipulated.
This didn't last because when the Le Cleric expedition came the French seized control of Santo Domingo pretty easily and even when expelled from newly independent Haiti they still kept control of the Eastern section until British/Spanish forces expelled them in 1808. French rule was bad and did the usual French Republican marauding (alongside later trying to reinforce slavery up to and including kidnapping children). The Haitians did invade multiple times, sacked a few cities (Moca, Cotui, etc) and depopulated the border areas in a scorched earth campaign. Not a good look for the much whiter and basically slave less north. Don't even think the Maroons liked it.
In any case the point is, the first unification was a drastically unpopular and unstable
French one.
The Second One from 1822-44 was built atop an unstable foundation that was doomed to implode sooner rather than later, and where circles in Santo Domingo were already talking about fighting the Haitian government as early as 1833. That we know of, could be earlier. Roughly about 1/3 of the population, mostly the few remaining slaves numbering about ~15% of the population supported siding with Haiti in 1821, and mostly clustered along the border (the other third wanted independence or union with Gran Colombia) On the Haitian side earlier as Boyer's coalition turned against him arguably as early as 1825, feeling him caving to the French was utter cowardness and the indemnity unsustainable and unjust.
Boyer's coalition as it was included balancing the bloated army from the former kingdom of Haiti (who wanted land and serfs) alongside the yeoman farmers of the south. Neither of them liked his attempt to enforce rural working codes that amounted to serfdom, and the Dominicans were especially loath to fall into that (ironically with the burden falling to former slaves in a colony that barely had any plantation agriculture). It was a compromise that pleased no one, and got worse as Haiti's economic condition worsened as the years went by and custom receipts weren't enough.
Long story short every class of Dominican society ended up isolated from his rule, despite the best intentions. The white rancher and landowning elite didn't like having upstarts and black people ruling over them, nor did they like the threat of land redistribution (ironically Boyer kept on delaying land reform until the mid 1830s, which annoyed ex slaves) and the closure of the university and other cherished institutions. The petit bourgeoisie, especially up in the Cibao were upset because now they were under a de facto embargo from a good chunk of the world. The freedmen and poor people of color/poor whites upgraded from slavery to serfdom and higher taxes. And the clergy was stripped of its lands and privileges. Anyone but the elite didn't like the government switching everything to French (as they couldn't speak the government language; ironically this made the Haitian government dependent on said elite they were trying to subsume and strip their land of).
This is not a recipe for long lasting control, especially when the population disparity was shrinking.
it seems insane on paper that Haiti wasn't able to keep control of what is today the Dominican Republic. i think all it would probably take would have been more competent leadership and perhaps some sort relocation of Haitians to parts of the island.
They tried relocation colonies, even as far as sending entire families to Azua. The problem with relocation eastward is that it weakened the Haitian state's presence as local towns further from Port-Au-Prince and Le Cap stopped caring about the governments authority and the army often wasn't interested in marching several hundred kilometers east.
Additionally the more people you move out of Haiti proper means less workers for the plantations. Its always been the goal of the Haitian state to have a strong central government to maximize usage of labor, which is made more difficult as the population spread out.
Of course the longer you hold it the more likely the US and friends are to intervene. (There were proposals to do so in the 1830s and set up a protectorate, again in 1844 and so on).
