I already have worked out a rough timeline of how would Spain and Portugal join.
1974: The Revoluçao dos Cravos. The right-wing military junta that has been leading the Estado Novo de Portugal for more than 30 years falls in a coup by left-leaning soldiers. The symbol of this revolution is the carnations civilians gave to the military insurgents. Democracy is established in Portugal.
1975: Franco dies. Juan Carlos I rises to the throne as King. For the last year, the Junta Democrática de España and the Plataforma de Convergencia, formed by alliances of all pro-democracy (and illegal) parties in Spain have been pressuring for the re-establishment of the democracy that was lost in 1939 after the victory of the Nationalist side in the Spanish Civil War. Both of them also advocate for a immediate breaking of the current legal system so that a democratic constitution may be written up. Meanwhile, in Portugal, the first democratic elections in many years, directed at the creation of the Constituent Assembly, go on, giving victory to Mario Soares' Partido Socialista.
1976: In Portugal, the first attempts to establish a true democracy work, with hard work by the politicians that wish for it to happen and going towards . In Spain, the Ley de Reforma Política, which will allow for the gradual reformation of the government into a true democracy, passes in a referendum by a wide margin, with more than 80% of positives votes.
1977: Spain sees its first democratic elections in many years: Adolfo Suárez, leading the Unión de Centro Democrático, wins by a large margin, with the left-wing Partido Socialista Obrero Español in second place. In Portugal, the first post-Constitutional elections start, and Mario Soares wins once more. In both elections, there is a surprising party: the Iberian Party, that calls for the creation of a joint Spanish-Portuguese nation so that both of them may be well heard in the world scene. They win 13 seats in the Portuguese Congress and 10 in the Spanish Congress.
1979: Spain goes through their second elections. The CDU wins again, but loses many seats. PSOE rises a lot, and the Iberian Party catches 25 seats, to the detriment of Manuel Fraga's Alianza Popular and the Partido Comunista de España.
1981: On 23rd February, extreme-wing elements within the Army attempt a coup d'etat in order to restore the Francoist regime. The Congress is taken by a group of 200 Civil Guards led by Colonel Antonio Tejero. There are only four deputies that do not hide themselves when the shots are heard: President Adolfo Suárez (who has presented his dimission), Defense Minister Manuel Gutiérrez Mellado (whom, even being 69 years old, is brave enough to face Tejero), PCE leader Santiago Carrillo and the Iberian Party leader Alfonso Guerra. This coup d'etat will be solved in less than a day thanks to the timely intervention of King Juan Carlos I, who manages to issue a speech in which he condemns the coup. However, as this is happening in the TVE studio, he doesn't know that tragedy has struck his family: in the Palacio de la Zarzuela, the official residence of the Royal Family, a group of pro-coup soldiers has entered and, accidentally, killed 18-year-old Infanta Elena, 16-year-old Infanta Cristina and, worse of all, the Prince of Asturias, 13-year-old Felipe. This will send the whole nation into mourning, as the Royal Family is well beloved in Spain. The trial against the coupers will see many of them sent to prison for more than 30 years each, and the killers of the Infantas and the Prince are killed by an assassin claiming to do this in vengeance for the children's deaths. It is soon established that King Juan Carlos had nothing to do with this: the King has been the whole time mourning next to his wife the deaths of their children.
1982: New elections in Spain and Portugal. The Socialist Party wins in both nations, but the great surprise is that the Iberian Party continues its meteoric rise. The potential entrance of both nations in the EEC is giving them wings, as both nations together will be able to fight for better standing in the world scene.
1986: Elections again in both Spain and Portugal. The Iberian Party finish their upsetting race by winning great majorities in both nations. They soon decide to hold referendums on whether a possible union between both nations is possible. Both referendums pass with more than three quarters of the voters favouring union. King Juan Carlos, heavily burdened by his loss of five years ago, decides that his time is over, and presents his abdication as King of Spain. Spain and Portugal join into the Iberian Republic. Its coin will be the Ducado, and it'll have Spanish and Portuguese as official languages, but as with the old Spanish Constitution, regions with other languages will be permitted to have them as co-officials. The nation will, curiously for a Republic, have two Heads of State: the first one will, naturally, be the President as chosen through popular voting, but the other will be Juan Carlos de Borbón y Borbón, in recognition to the hard work he went through for so many years to restore democracy in Spain. The former King, at first, wanted to reject this honour, since he would rather live the last years of his life in peace. However, after an impassioned speech of new Prime Minister of Iberia Alfonso Guerra, in which he tells the great accomplishments the King has done in his life, the whole Congress of Deputies convening in Madrid (which will be the capital of Iberia) rises into a very long applause and cheering for Juan Carlos. It isn't long after this that an spontaneous manifestation starts in the most important cities of Spain, all of them cheering for Juan Carlos and offering their support for the man that lost so much and yet still gave a lot for the country. The images of King Juan Carlos I breaking down and crying like a child in the shoulder of his wife, Queen Sofía, go around the world, and give him great popularity in the whole nation, who has always liked him and now see that, even with such a burden on him, he is still a person like the rest of them.
1989: The Berlin Wall falls. As the Soviet Union breaks into several nations and the United States does the same, the equilibrium between the world's nations is broken.
1991: France, having undergone several years as a Socialist Republic, decides that the best thing it can do right now is to expand, since now there isn't anyone able to check on them. They choose Iberia, thinking that such a young nation will be easily pushed over. This will be a great mistake.
1993: After a hard war lasting 1 year and a half, the Socialist Republic of France and the Republic of Iberia make peace. France loses the French Pyrenées and the region of Aquitaine to Iberia for their role in starting the war, and this comes at the same time the regions of Alsace, Lorraine and a couple more secede from France and join the Central European Union.
2000: Present day. Currently, the President of the Republic is Javier Solana, and the Prime Minister is Joaquín Almunia. Juan Carlos de Borbón is still the Honorary Head of State of the Iberian Republic, and travels around the world, always making use of his diplomatic skills to attempt to broker peace between nations. Nowadays, Iberia is more united than ever, as Iberian nationalism has been a part of the culture ever since the Iberian Party rose to power.