Some people believe that most Dominicans probably have Haitian ancestors, but in reality Haitian migration to the Dominican/Spanish part was, until the 1990s and 2000s quite light.
From 1697 to 1801, even though these were not Haitian proper (unlike Dominican sense of identity, the Haitian sense of ide tity arose after their independence not before and as such, we can't refer to people on the French side prior to 1804 as Haitians). There was some migration of slaves that escaped from the French part and this was even encouraged by the Spanish slave laws which were some of the most linient in history that made it easy for slaves in Spanish colonies to gain their freedom. Regarding the slaves from Saint Domingue, they were granted their freedom ass soon as they crossed into Santo Domingo (current DR). This was a point of contention with the French because they demanded that their runaway slaves be returned while the Spanish objected. Runaway slaves from Saint Domingue became free men and women, and subjects of the Spanish Crown with equal rights as was given to the Spanish themselves.
Many of these people became subsistence farmers and were not just left alone by the Spanish authorities, but also their freedom was protected by the Spanish Crown itself with the French understanding that any incursions into Santo Domingo in search of their former slaves would be cause for military retaliation because they were effectively attacking free Spanish sujects.
There are no reliable estimates how many people made use of what can be called our very own underground railroad, but it couldn't had been sufficient to alter the character of the Dominican population. Some former towns, like San Lorenzo de Los Mina (today its a neighborhood in Santo Domingo Este) was settled by runaway slaves from Saint Domingue. That town was created with permission of the Spanish authorities and they were left to live their lives as free men and women with equal rights as the rest of the Spanish population.
From 1801 to 1822 whatever amount of Haitians that migrated eastward must had been negligible. First, the military incursion by Touissant in 1801 and later the assassins Dessalines and Christophe in 1805 didn't left many Haitians on this side. If anything, whatever changes the Dominican population startd to experience was due to the emigration of some white, mixed race, and anyone else that felt threatened by the bloody invasions, especially the terrible one from 1805 when the Haitians attempted to commit genocide on the peaceful and innocent Dominican population.
From 1822 to 1844 the Haitians controlled Santo Domingo (current DR) with tens of thousands of Haitian military men. That was definitely the largest influx of Haitians into Dominican territory, plus the 6000 African Americans that arrived in the 1820s although most went back to the US; but, the occupation failed due to stupid laws such as prohibiting the Spanish language (during the French occupation from 1802 to 1809, everything was done in French and in Spanish), ruptured the relationship with the Vatican, tried to limit the holidays and cockfighting (before baseball cockfighting was the preferred sport among Dominicans), tried to taxed the population to pay the debt to France (Dominicans outright rejected paying for that under the excuse that we were never subjects of France, not even during the French occupation of 1802-1809), etc. To add salt to injury, Boyer's regime didn't give provisions to the Haitian troops stationed in the Dominican side and they developed the habit of demanding from the Dominican poppulation to give them food and other stuff, in many caases the Haitian troops engaged in outright theft especially from Dominican campesinos, in the process earning their repudiation from the population at large.
From 1844 to 1920s Haitian migration was also negligible. The fact that not a single foreigner that wrote about their visits to the DR (including Samuel Hazard in 1871) mentioned the presence of Haitian colonies anywhere in the DR is a reliable testament to this. Samuel Hazard did mentioned that there wer many black immigrants from the Britsh Caribbean in places like Puerto Plata and even mentioned the African American colony in Samana (he obviously mentioned them because they were numerous enough to be noticed), but nothing about a visible presence of Haitians. Also, the Census done in the early 20th +entury by the Americans had Puerto Ricans as the largest colony of foreigners in the country and Haitians weren't in the top 5. Most of the black foreigners were Cocolos from the Lesser Antilles.
From 1920s to 1980s Haitian migration was mostly controlled and never surpassed 100 000 at any time, they were overwhelmingly men and were restrained to the sugar plantations. Not much illegal migration took place, especially during the Trujillo years.
From 1980s to 2000s illegal migration picked up as political instability took over Haiti after Baby Doc's dictatorship collapsed. Since the 2000s the flow has increase and after the earthquake the DR has experienced the largest influx of illegals in all of its history, the colonial part included (the ruaway slaves from Saint Domingue).
Until the mid-20th century Haiti was better off than the DR and the Haitian population density was within the natural carrying capacity for the size of their territory. There were no pull or push factors for Haitian migration to DR and, not surprisingly, the Haitians didn't migrated eastward in sizeable numbers.
In colonial times there was a pull factor and that was automatic freedom as soon as the slaves crossed into the Spanish side, which was bigger than the current DR (53 000 km2 vs 48 000 km2 due to Haitians stealing 5 000 km2 that rightly belonged to us- valleys of Guava, la Miel, etc). But, their flow was not that great to alter the character of the population, otherwise at least the chroniclers from the time would had mentioned this in their writings.
Post mid-20th century an increasingly prosperous DR has become a pull factor while the falling apart of Haiti has become a push factor on Haitian migration and explains why its right now that the Spanish side of the island is seeing the largest influx of Francophone people.
Anyway, I think its safe to assume that most Dominicans don't have Haitian ancestry. The Spanish side of the island has been majority mulatto and freesince the mid-1600s, in the 1700s we had the largest influx of whites (Spaniards from Canary island accounted for much of the population growth during that century), in the 1800s there was an exodus of many whites, an influx of blacks, and after 1844 an influx of whites and after 1870s an influx of blacks. From 1930 to 1961 we had an influx of whites, post 1980s an influx of blacks. During those times, much racial mixing has taken place, but the current migration flow is uncomfortable because of Haiti's history of coveting the Dominican Territory and of using its people as chess pieces in its island expansion ambition, as we've seen with the loss of the 5 000 km2 of Guava.
To all of this we must add that among certain Haitians there is a feeling of hopelessness for Haiti and, at the sametime, envy for the progress the DR has achieved compared to them during the past half century. This is why its quite often that, at least it has been my experience, when some Haitians speak of Haiti's development, they always mention the DR as a sort of yardstick that they use to judge their own backwardness and the lost opportunities they had. I have never heard a Haitian compare their country to Jamaica or Bahamas or Trinidad or Barbados, all countries that have also developed much more than Haiti. Its the Domin ican development that catches their attention and, in some cases, I say envy too.
A few years ago I was reading an interview that was done to a Haitian and when asked about why the DR has gone ahead while Haiti has not, he said (and this is the only part that I still remember: "they still have kids walking barefoot."
In DR1 fashion; 'nuff said