The Christians didn't invade Spain. The people of Spain converted to Christianity. The Muslims on the other hand came as invaders. The Christians, therefore, being the descendants of the native people of Spain had a valid claim to the land, whereas the Muslim Moors, as invaders and oppressors, had no claim to it. The Spanish people fought a long and bloody struggle of 700 years, the reconquest, to take back their land from the Muslim oppressors and in doing so saved all Europe from Islamic rule.
The Western Goths (Visigoths), who had nothing to do with that part whatever, invaded the Roman emprire in the beginning of the V century. Rome was sacked, and Iberia concured almost entirely. Shortly thereafter, their King was converted to Christianity. In another hundred or so years, Moores concurred all of Iberia with the exception of the Basque country; they called it al Andalus.
Spaniards today are a mixture of Goths, Berbers, Slavs (these were imported as slaves --- which is how the word "slave" came about), Roma (Gypsies), converts from Islam and Judaism. Except for the Basques, whom even Romas could not concure, there are no indigenous people there. You may want to read up on that people to understand who where "people of Spain" who converted to Christianity.
One objection I would raise: you seem to be siding with co-religioninst, whereas you should be siding with right agains wrong. This shows, in particular, in your perception of Moores as "oppressors" and rather warm perception of the Catholics of that period. As I said earlier, Moores in al Andalus are usually sited as a historically significant example of tolerance and harmony; they ruled Iberia for almost a thousand years (most parts were given up in XII century, but Granada fell in 1492). Most importantly, you may want to gather more facts about that period.