I don't know about the West Indian Parade ordeal, but the schism that exist between much of the rest of the West Indies and the Spanish West Indies could be due to two things:
A. People must remember that in colonial times, each colony identified with its colonial 'homeland' and the nationalism that eventually developed in places like Spain, France, Netherlands, and the UK reappeared in its colonies. For much of colonial history (especially after the Spanish Armada was 'defeated' by the British - personally, I think the weather had more to do with that -), these colonial powers were not keen to seeing eye-to-eye in Europe and where ever they had a presence in the rest of the world.
This mistrust could very well be a residue of the regional colonial experience. There are plenty other examples, such as Sir Francis Drake. To me, he was a villain, scum of the earth, good for nothing, should had never been born; but I've met plenty of historians of the Anglo-Saxon cultural variety (from the English-speaking Caribbean and the US) that attempted to make Sir Francis Drake appear as some truly great figure. And despite understanding why they see him in such positive light, I still find it ridiculous.
B. There is the economic issue. Except for Trinidad and Tobago, the DR has tremendous advantages with every Caribbean country when it comes to trade in almost every single economic sector. The DR trade balance is positive even with Puerto Rico - and I mention this because in theory, given PR's relationship with the US, the number of US firms with operations there, and the suppose greater efficiency everything is done there; PR should be the one with a surplus rather than a deficit in its trade with the DR. Given that all those islands, particularly the ones in the lesser Antilles, have an economy that is only a tiny fraction of the DR's and the advantages the DR naturally has in almost everything, they are probably afraid their economies will be dominated by Santo Domingo based firms. That can have several implications, and what I stated in section A may well be a motivating factor behind all of this as well -- ie. the notion that the Spanish-speaking Caribbean will become the central focus of the English-speaking Caribbean economy.