Pardon my error, it should read "third invasion by Haiti" not "of Haiti"
Here's a recent answer of mine about the failed attempts of Haiti to reconquer the Dominican Republic, where I briefly talk about the 1855-1856 invasion. To be fair, the Haitian army did not "flee at the first shot". The campaign started on 10 December 1855, with the Haitians having some success in the first weeks, but Dominican counter-offensives routed Haitian troops in several battles and Soulouque admitted defeat on 27 January 1856, blaming traitors in his army. The reasons usually given for the rout were that the campaign was ill-conceived, lead by a "lethargic" Soulouque (Michel, 1932), with troops that were badly equipped (thanks to corruption) and had no reason to fight. Soulouque had several generals shot during the campaign (including César Dessalines, grandson of Jacques Dessalines). Fabre Geffrard, the general who led the coup against Soulouque early 1859, was one of the few officers to have won battles in the two expeditions against the Dominican Republic in 1849 and 1855, and his popularity in the army was caused in part by the care he had shown for his troops.