The Islamic conquest of the Iberian peninsula was before Spain and Portugal and you know it. The population there were not called Spaniards back then; they were vandals, hence Andalusia.
So it's not the same lineage albeit being the same land. Correct me if I am wrong. But that's beside the point.
Now, why did they pass Gibraltar in the first place? It's a mixture of imperial hopes of the polity that ruled (Umayyads) and the obligation to free people from earthly shackles.
Now, we can debate the polity ad nauseum, but every empire before and after expanded for different reasons. So, it can't be just Islam as a religion. If that is your case, we're discussing the wrong topic.
For the second point, freeing people from earthly shackles, we can debate. But first let me clarify a few things. Islam's first and foremost idea is monotheistic. Allah is the only God, the same God Jews and Christians worship (the, so called, Father, to be particular). It follows the lineage of the Bible, whether it be books or prophets. It confirms many ideas in the Bible and believe in the prophets in it. As Muslims, we believe that the Torah and the New Testament are the words of God (although corrupted through centuries of translation and people changing/ adding to/removing from it). Jesus is a highly revered prophet, born to a virgin Mary. All these facts about Islam can't be meaningless to you.
So what shackles am I talking about? All these earthly insidious problems are considered shackles; murder, usury, adultery, alcohol and drugs, lies, robbery... Etc. If a society does any of these, as a Muslim I am supposed to warn them and invite them to do better by being Muslim, or at least not do better and remain following their faith. There is no compulsion in religion (Quran 2:256); you're the master of your belief.
Other shackles include taxes, in the first Islamic governments, there were no taxes on Muslims. Taxes are considered compulsory theft and a major injustice, and are prohibited. The only tax mandated is on non-Muslims (2.5%) for protection, because they're not required to join the army, and they're left to manage their own lives.
The original form of governance in early Islamic society is that the government is responsible for defense, execution of rule of law as mandated by judges and scholars, collecting Zakat and distributing it to rightful deserving people, and, finally, ensuring Waqfs are respected and sustained. Everything else is left for the people to manage. I think that's a form of governance you would like, isn't it?
"Islam was spread by the sword" is also not true. Egypt, for example, who's 90% Muslims today, remained majority Christians for 6-7 centuries after being included in the Islamicate.
Another anecdote. Early Muslims handed Damascus back along with the protection tax they took, because they couldn't keep the byzantines from taking the city back. They didn't pillage nor did they rape. They took the land, in the first place, because the byzantines were taking too much tax, and they wanted to free the people from that.
Sorry, for the very long post. I will order the Korean tonight, but I do hope you keep an open mind. @Viktor recommended books, but I will recommend Karen Armstrong's Muhammed A Prophet For Our Times.