I can't answer your question specifically. I have a friend who is involved in Mission work in Haiti with a group based here in the States
. Based on conversations with him relative to the current economic conditions in the country, I'm not sure general aviation, especially for foreign visiting pilots, even exists in Haiti, Wikipedia lists 17 airstrips within the country. I would assume they are mostly used by missionaries or medical personnel. Next time I see him, I'll ask him, although he is not a pilot.
Personally, there are some countries that I would like to visit, but I don't think I'd want to park my airplane in some of them for fear of theft or other mayhem.
I think your idea of landing in DR and then driving into Haiti might be the better idea.