This isn't a balance problem because you're starting in 1066. In 1066 the Christian kingdoms were weaker and poised to lose. The only thing that changed the situation was the
Reconquista which was a huge horribly complex thing that involved lots of other Europeans and lasted over 700 years and can't even begin to be represented in-game.
This completely false idea of the situation in Iberia is EXACTLY the reason why this problem exists in game.
Let me put this in simple terms: in 1066, the Christian Kingdoms were in a position of TOTAL MILITARY SUPREMACY over the Muslims. By this I mean the Taifa Kingdoms were PAYING TRIBUTE to the Christians not to get invaded, and is also the reason why the Jimena brothers took their time fighting each other: they had time and NO pressing military threat from the South. The Christian greatest enemies were themselves.
In fact, by 1066 it was just a matter of WHEN, not IF, the whole of Iberia would be Christian. And that is why, once the Jimena interstruggle (plus some rebellions, like that of the Count of Portucale in 1072) got sorted out and the Christians started to move South again and conquered Toledo in 1085 that the Taifa begged the Almoravids (i.e. Mauretania) to come and help them. The Berber arrival did balance things out for a while, but not that long: by 1139 the Count of Portucale ALONE was able to handily defeat the MAIN Mauretanian army [his levy was 1,500 men, if you want to know], and by the battle of Las Navas de Tolosa the Berber power (which had been reorganized by a second wave of reinforcements from North Africa, that of the Almohads) was definitely broken by nations that, ultimately, had far, far, FAR greater military strength than the Muslims ever managed to field in Iberia.
There are many reasons for that:
1 - Unlike in CK2, the VAST majority of the population in Iberia was Christian, not Muslim, monotheists having proven to be especially hard to convert (there is a reason why there are still 10 million christians in Egypt today, let alone 1,000 years ago); that meant that Muslim lords had serious problems in getting reliable levies to fight Christian foes. They relied mainly on their Muslim light cavalry, which was composed of landed gentry, which lorded over fairly extensive landed possessions in order to afford a horse, and was not very numerous;
2 - This is because the Iberian Peninsula had been CUT OFF from the main Muslim world when the Umayyad Caliphate was overthrown by the Abbassids; Iberia was the only area of Islam where the Umayyadds kept power, and was thus a separate Caliphate for 250 years (the Taifa kingdoms we see in 1066 represent the break-up of that rump Caliphate, which occurred in 1030).
3 - The fact that the vast majority of the population was Christian meant that the Mulsim rulers had to be careful not to antagonize them; they thus taxed them little compared with the Christian North (in fact, by 1066 the county of Coimbra had been conquered less than two years ago; by the end of the year its population would be in rebellion, as their taxes had been raised to the Christian 'norm', which was FAR more than what they were used to pay under the Muslims). Since the bulk of the income came from agriculture, this means that many Muslim taifas were actually at an economic disadvantage.
4 - This is also why the Christian Kingdoms managed to easily assimilate the southern regions - no 'wrong religion' penalty, the populations were easily integrated.
5 - Unlike the gigantic tech bonus CK2 gives the Muslims in every area, Islamic technological advances were mostly in trade and shipping construction. That gave them more income from ports and a (useless) sea advantage, but only some areas actually benefitted from this (like Lisbon, Cordoba, Seville, Valencia... almost the only true city in the interior was Toledo, and it could do little to hold the Christians off). It means little to get extra troops, when you were seen as 'outside' the 'proper' Islamic world (and because of this, when the Mauretanians arrived in Iberia, they ATTACKED the local Muslim Emirs who had asked them to come, who then had to turn and beg the Christians for aid).
In other words, the situation in Iberia is completely broken and starts off in a totally ahistorical way because the local history was not properly researched. There is just the incorrect notion that "Muslims were stronger", and they were set up in the game as such.