Calling these ruffians "mercenaries" is an insult to true mercenaries. In 1978 the Dominican Police Force had 282 men and the neighboring countries, including USA are members of the regional security system that promised to provide security assistance. The whole "Coup" was a fantasy from day 1.
That why it doesn't make sense to me. How was a handful of thugs supposed to even win a temporary victory in Dominica?
How would this affect Reagan and the Conservative party along with the US? It’d be a blackmark of incompetence and would taint the GOP.
How? David Duke was a registered Democrat until the late 80s (and had run for the Democratic nomination for president in 1980), and Don Black was associated with a variety of minor far-right parties, so he wasn't a Republican either. What will happen is an investigation of the government agencies in question and no doubt some people getting fired for their incompetence.
Given the only American casualties would be neo-Nazi terrorists getting killed on foreign soil while committing crimes, I don't think the impact would be particularly large compared to other events of Reagan's first term.