As early as 1589, the Tohorinese Isle -or Las Palmeras- as it began to be called then, proved to be useful as a bread-case and as a base of operations whose location was of a heavy strategic importance for controlling the Caribbean, which in turn would prove vital in conquering the mainland Americas. It proved an important logistical support during the conquest of the Aztecs in 1572.
Because the native Tohorinese were immune to Old World diseases ever since our contact with Rome, unlike the Native Americans, there was actually a population growth due to so much intermarriage between the cat-folk and European settlers (and to a far lesser demographic extent, African slaves). An economic boom at the end of the century occurred due to the consolidation of urban works related to tending ships and catering to convoys. The large native work force and the existence of wages eliminated the need of slavery but also caused what little African slaves that lived here to be integrated into urban areas and so much assimilation caused an unwitting end to many West African customs. Spain continued to import slaves to other parts of the Americas though.
Records from tree trunks indicate that a small Gamma Ray Burst affected ozone layers above the 45° Parallel North hampered the agricultural output and growth of Northern Europe and plunged Europe into further wars and migratory patterns. A miniature Ice Age ravaged Europe for the second half of the 16th Century. This also gave Spain time to consolidate its monopoly on what is now Latin America and the Caribbean uninterrupted of other powers' intervention.
The security of the Spanish Main was threatened in the middle point of the 17th Century, which was seen as a cherished moment for the Hispano-Tohorinese military aristocracy, which yearned to prove themselves and gain glory. Many members of the Spanish-Neko aristocracy rose in ranks by attempting to mop up Anglo-Dutch-French buccaneers among smaller islands. Or alternatively by also turning to piracy by being privateers who raided Portuguese ships with diamonds and gold en route from Brasil to Portugal.
Several pirate raids among coastal cities spurred the need of a local militia force, the first of its kind in the Spanish Colonies. The zealous Tohorinese militarists are credited with diminishing the pirate menace after the 1690s.
1655; Island of Santo Domingo/Nanba resisted Oliver Cromwell's attempt at taking the island. However the British temporarily occupied the Cayman Islands until we re-captured it in 1666. Nanba also resisted the attempts of French settlers to take the island, though at a very heavy price. Ironically these victories, by the Hispano-Tohorinese militarists, caused a flurry of rage in Metropolitan Spain as they felt snubbed.
18th Century: "The Era of Challenges"
The 18th Century saw the Home Island's position as a lucrative bread basket challenged by the British African slave trade, which dramatically increased the agricultural productivity of their 13 Colonies and the Bahamas and by British threats to open the Spanish slave trade...which would diminish Madrid's dependency on Tamanshan's labor pool.
The War of Spanish Succession itself also put the delicate indirect rule of the old Habsburgs in danger, as the French Bourbons were used to more centralized control. Tensions increased decade after decade within the Home Island Colonial Office over the jurisdiction of what Spanish bureaucrats had. The opening of Spanish migration to the Home Island, meant to peacefully change the demographics through sheer inter-mixing, began in this era. Something which definitely ended the old economic order of the island between the peasants and the military aristocrats.
During the 7 Year's War, Ethnic Tohorinese garrisons in Havana resisted the British onslaught and also rebuffed a British fleet in the Home Island's Shirya Strait -albeit at the costly price of having parts of the city and Navy in ruin- and this meant the 7 Years' War ended in a partial stalemate between Spain and the British; though Spain still had to sede economic concessions to the Great Britain. The event evened out Britain's advantage in the diplomatic scene but most importantly, won the Ethnic Tohorinese a mix of prestige and dread among Northern Europeans for Spain's "Asiatic Hordes" as the British were more anxious to maneuver around Spain in any future conflict. The "Importation" of Colonial Auxiliaries became a major source of contribution of the Palmeran Isle.
This battle also gave a glimpse of a growing feeling of fanaticism among the mixed-race military aristocrats, who went against Spanish orders for surrender and turned to house-to-house fighting and tunneling around adobe buildings. British naval bombardment ironically also turned rubble into hidden positions and contested fortresses in urban combat. Our revenge against the British Empire was fulfilled in 1781, when the Palmeran Isle's Naval Infantry helped re-take Gibraltar by scaling it's unprotected eastern side*. A daring operation many thought impossible and whose magnitude in cunning and surprise was not repeated until the American landings at Incheon! In hindsight, the daring victory was almost for naught, as Britain still negotiated use of the Strait in exchange for help against Napoleonic France decades later.
*Note: Gibraltar isn't as steep as it is IRL; because a mysterious object crashed into it 12,000 years ago.
1812 to 1909: Loyalty and Rebellion
The Palmeran Isles -economically semi-dependent on raw supplies and cereals of the mainland- vehemently went against the independence movements occurring in the Americas; and it willingly remained the only loyalist colony in the Spanish Americas.
The problem in Cuba was ironically caused by the Tohorinese Militarists a century before: their victory in Havana in 1761 assured the slave population (which would've been dramatically increased by British occupation) remained low and the local landowning elite became haughty after realizing that they didn't need Spain's presence to control their servants. Once again, the ethnically mixed Hispano-Tohorinese Naval Infantry proved its worth to the Spanish Empire, brutally crushing the 1st Cuban independence movement despite suffering from Yellow Fever and malaria. Spain would retain its Caribbean islands for a few decades more.
After the Independence of the mainland Latin American nations and unsuccessful attempts at helping Spain re-conquer México, Perú and Greater Colombia the Palmeran Isles entered a period of economic stagnation in which our main link was just Spain. Though we managed to be more industrial than Madrid and Cataluña in Europe, our wealth didn't compare to the streaks of productivity of yore nor did it equal the pace of industrialization in the UK and France. A shift to sugarcane and chocolate (from the Caribbean) processing took over some manufacturing areas even if its net worth wasn't as good as the weakened shipyard building industry or the military subsidization of jobs relating to convoy duties which kept the economy going during the height of Spain's overseas empire.
Politically, in order to prevent further treason or rebellions, Spain began to concede more noble titles to the mixed Neko-Human military aristocrats, even if they felt they eventually hit a glass ceiling, and their dissatisfaction eventually rose. Some steam was allowed to escape, pressure was diminished by the counterweight of a more westernized civil authority which modeled itself after parliamentary institutions back in Mainland Europe, and also by more liberal factions of Spain. However, both the Militarists and Civilians surely would have rebelled by the 1900s if it had not been for one unforeseen external factor: the Spanish-American War.
After the war, the Palmeran would-be independents were exhausted but so was Spain. Fearing more bloodshed, both sides settled for a transitory 'Autonomy', after which a Referendum for independence would be cast. A large and more modernized portion of the "Spanish" Navy remained ethnically Hispano-Tohorinese, giving the Isle a huge leverage in the negotiations. Both Civilians and Militarists gathered around the Imperial Figure to declare that Spanish tutelage was no longer necessary and that the old monarchy could act on its own...that is to say...once again a ceremonial figurehead shadowed by local military, financial and bureaucratic cliques.
Externally, American pressure against Spain continued, and at their behest (and thirst for new markets) the Palmeran Isle obtained a fuller autonomy from Spain in 1905 in order to appease American investors...who were generally not liked due to wage issues and their lack of connections in the local elite. This opportunity wasn't completely negative and industrial growth overshadowed Spain's, in great part because of investments made to the electric industry and fish processing and grants issued by the US after the war, ironically enough, which also opened a path to normalize relations with the Isle. An increase in male immigration seeking economic opportunities from Spain led to a population boom as Las Palmeras grew to be a major commercial node and shipyard. Relations with Spain and fiscal subordination even as an autonomous region became more tense as we had finally grown too big for them.
And so, a formal end of direct ties to Madrid began in the 1911 after a 61% vote favored for separation; our Independence was praised for being a nonviolent and benignly non-violent process.