It's not only the Dominican Republic that is problematic. One of the sugar plantation owners whose labor conditions were exposed in the films owns plantations in Florida that also import Haitian migrant workers on temporary U.S. visas harvest cane. In areas where sugar is grown as a main cash crop at the expense of diversified agriculture the health of farmers tends to plummet. Children raised in this environment often live on little other than chewed sugar cane which is a disastrous diet for preserving health and welfare. In 103 countries sugar growers face a myriad of occupational health hazards, made worse by their poverty and lack of access to health care. Wages in the industry are very low, yet jobs in sugarcane production are among the most hazardous in agriculture and in some cases, farmers do not earn enough to provide enough food to cover the calories burned on the job.
Isolating sugar produced in unethical conditions can be difficult. The commodity is sold on the market to manufacturers who may buy from many sources depending on prices. Cane sugar still accounts for 60-70 percent of all sugar consumed in the world and in the US, domestic production of cane sugar still falls short of demand. We still import a fifth of our cane sugar from the developing world. The by-products of the industry may wind up in producing rum or ethanol. Ethanol production from sugar cane has its own issues. The burning of sugar cane to make ethanol has had a toxic effect on the people living near such refineries in places such as Brazil.
There is a corporate responsibility organization called "Ethical Sugar" which represents progressive sugar growers who use fair labor practices and sustainable growing techniques. My suggestion is that people who are concerned about the origin of their sugar should assume that if it is cane sugar and not produced by a fair trade manufacturer (Rapunzel is a fairly well distributed, if pricey product) that it probably was farmed at great expense to human life and environmental welfare.
The easiest and cheapest thing to do is to stop eating sugar. Use local honey and fruit to sweeten if you must or switch to an ethically produced brand. By the way the so-called turbinado sugars (Sugar in the Raw) often seen in health food stores, though less processed is not necessarily any healthier or more ethically produced than plain, white sugar. Because of the importation of migrant labor to U.S. sugar producing states Florida, Texas, Hawaii and Louisiana, the problems of labor conditions can still persist. At this point Sugar in the Raw is not part of a fair trade organization. The sugar added to most processed foods in this country is refined from corn or beets and may have its own set of problems in terms of environmental impact and public health, but at least its not the product of slavery or near slavery conditions.