Hmm. What would need to happen in Al-Andalus for it to become a solid established power like the christian kingdoms that came after, with the ability to project power and establish a lasting presence in the western mediterranean? I mean, so it becomes a kind of "Ottoman Empire of the West", with the capability to eventually take Rome?
What would
technically need to happen would be something along these lines
Political unification and no regular revolts; no reliance on foreign troops; no important foreign pressure; cultural/ethnical unification, not too strong neighbour.
That alone would be enough.
Now, I don't think it would happen.
Ottoman Empire was quite particular in the Arabo-Islamic world, mostly because of its longevity : only the Abassid Caliphate had a similar lifespawn and 2/3 of it consited of being under the thumb of someone else.
The specific issues about surviving Al-Andalus make a similar path unlikely to ever appear.
- Political unification.
Medieval Arabo-Islamic structures tended to be unsable at a quite important point.
Even in the most prosperous cores, emirates/dynasties were changing quickly while entities as Byzantine Empire or feudal realms (both being subject to regular revolts, as Al-Andalus), and know more important succession crisis than these.
The lack of a true rule of law on the palatial structure of Muslim more important states, or the almost entierly dynastic basis of these...
Basically, when a Muslim ruler is strong enough to impose his authority (as Abd al Rahman III), things can go relativly smoothly.
When it's not the case (powerful neighbour, regency, someone stronger appear, etc.), Arabo-Islamic institutional structures aren't strong enough to provide a real support.
Simply said, the tribal and dynastic structure of Arab empires/emirates made the idea of a state (and subsequent structures) as independent from palatial authority had to emerge.
It can be changed, of course, but would requires a PoD far enough to deal with Arab structures (a more important Byzantine influence, as for Ottoman Empire for instance), that would butterfly enough of world history to make conquest of Spain butterflied as well.
Because of the factors mentioned below, political fragmentation was even more important in Muslim Spain.
-Reliance on foreign troops.
That's was one of the bigger problem of Al-Andalus : Muslims at first represented but a tiny part of the population. In 740 you may count of 15 000/ 20 000 Muslims, mostly Berbers. (After the arrival of syrian djunds in 742 : maybe 20 000/ 25 000)
And of course, they weren't all fighters (critically with Berbers that formed the main garrison, and just abandoned them during the Berber Revolt).
More importantly, these weren't the personal army of the ruler of Al-Andalus or particularly loyal : part of Syrian djunds by exemple, revolted almost as quickly they came in Spain. (Not helped by the tribal infighting, see below).
In a structure where the ruler is a gatherer of troops, a military ruler, but doesn't hold a real political control over these...(Even the urban militias didn't really obeyed the Caliphes) Eventually use of mercenaries and/or personal enslaved armies (Saqaliba) was necessary.
Of course, inviting foreigners that doesn't really mix with the population, are a drain for your ressources while they can reckon the land for a possible raid or takeover, is eventually a bad idea; every late roman emperor would tell you so.
This is, and here we have an huge perverse effect : less the ruler have support, more he's forced to use mercenaries. And more he's using mercenaries...etc.
Almanzor's rule is quite interesting on this regard.
-Ethnical issues.
More than in the rest of Arabo-Islamic world, this played a lot in Al-Andalus.
As said, Arabs formed only a tiny part of the population. 5 000/8 000 on a population of 3.5 millions.
And they were of course divided themselves along tribal or regional lines (the famous Yemenit/Syrian divide).
It's why they eventually choose an Umayyad. We could have guessed that getting rid of Abassid rule didn't necessited to choose a "loaded" claimant. After all, the province was already independent de facto, and Arabs nobles didn't really had a thrilling souvenir of Umayyad rule.
But, critically after a revolt that threatened to push them back into the sea, they needed someone that incarnated the Arab interests. And if Umayyads had one thing in mind when they ruled, it was to preserve that.
Even Hisham II legalized the situation de facto were Berbers, even converted, had to pay taxes reserved for non-Muslims.
Eventually, it meant that only Arabisation was the measure of social advencment rather than Islamization. Social conservatism, tribalism, etc. lead to a situation were even arabized descendent of converted weren't assured of the perenitty of the power they could obtain.
Hence, partially, the late IXth/early Xth revolts. It was at the point some muladi even converted back to Christianism.
Let that sink in : some muladi leaders feel that, in order to preserve their power, it was simpler to convert back to Christianism.
Eventually, and it made an Abd al Rahman III necessary, things went relativly better...For muladi. Ethnical division were maintained, not always lessened.
As an exemple, during the siege of Cordoba by Berbers during the Fitna, being Berber was enough to get you stoned, man, woman no matter.
You could say : well, you could have Arabs being less about "Arabity".
Technically, again, yes. Realistically, it wouldn't make much sense.
In a distant province, cut from Arab reinforcement since the 740's, forming a minority within the minority, and just avoided a Berber bullet in 740/41... It would actually make their rule more instable.
Of course, cultural and institutional changes could appear earlier (I would point out, nevertheless, that as long Arab is the real quranic language, Arab would still have a supremacy over other cultures in what we call
Arabo-Islamic world).
You'd need quite an earlier PoD then, giving the relativly narrow window of opportunity for a conquest of Spain (you won't have an everlasting civil war, coupled with a relativly not troubled Maghreb, without talking of course about the piece of luck that was the death of the ennemy ruler).
- Strong neighbour.
Ottoman Empire did have that, admittedly, but not really in its infancy (except if we count Mongols, but...). Whatever answered to the name of "Romans", Serbs, Hungarians, other Anatolian states...
All of that didn't exactly represented a threat or an actuall opponant. You have to reach Austria and Persia to really have something hard.
In the meanwhile, expansion and dominance is relativly easy.
Al-Andalus, on the other hand, almost immediatlly had to deal with Franks, that were going trough a process of unification since the VIth century.
I point out that Franks beneficied from better demographics and relativly better unicity at this point. (That's the difference between being an ethnic minority ruling over 3.5 millions, and a native elite ruling over 8 millions).
(Again, such unification can be butterflied away, but you'd need a PoD butterflying away Peppinids control of Meuse region to be efficient, meaning a VIth PoD, etc.)
Even northern Christian states could represent a threat.
It's not even a matter to have Galicia/Asturias being conquered by Arabs : they
were IOTL, but there was simply no real way to keep control on it.
Too much isolated, too much mountainous, too much costly for low profits.
If you add both raids from northern Christian states, and the fact revoltees regularly joined up with Christian kings (as Ibn Marwan)...
And I didn't talk about Fatimids, that formed a persistant threat. Not only because they supported rebellions (as Ibn Hafsun's), or of a more simple threat of invasion, but because they cut out trade roads at their profit and by conquering and taking control of Maghreb, they cut out Al-Andalus from a source of military manpower.
It's basically why Abd al Rahman claimed the caliphate : to fight back what was seen as an heretical threat for his dynasty.
At some point being in a peripherical position, on a really newly conquered province, forming only but a minority of the population, and having faulty institutions, wasn't going to work.
You can modify some of these features, while at the cost of a really early PoD (Out-of-the-box reforms would not only not work, but provoke a massive outcry ending with the head of the reformer on a stick), but all of these?
I wouldn't say it would be completely without effect--you're likely to see the papacy as we know it, nipped in its infancy,
Why? It would be hardly the first time Rome get sacked, and a temporary conquest wouldn't be that different.
Hell, the basilica St Peter, the seat that technically gave his supremacy to the pope was sacked, and it wasn't considered as a sign papacy had recieved his punishment.
Papacy wasn't a super-uber-centralized bureaucracy that once Rome lost would crumble under its own weight, critically not before Carolingian and Ottonian times.
Even if the pope and all the cardinals were killed because Muslims would be ev0l, and admitting Arabs have an interest taking Rome once raided (Yay for the conquest of provincial cities without really maintained defensive system), the structures to make the pope an unifying and dominant features (basically, carolingian-ottonian conception of papacy, and Xth reforms) would still be there (unless we're arguing that once Rome held, Arab pull a wank and devastate post-carolingian kingdoms).
Simply said, as long you have an imperial structure to back papacy and retake Rome (again admitting it's likely to have an emirate instead of a safer, more defensible outpost on the Tiber), a cesaro-papist conception of imperial power, and a religious movement promoting ecclesiastical power face to nobility (that appeared in southern France, so normally relativly safe from a sack), you'd have roughly similar outcome.