In this period, the Genoese crushed the Pisans, the Venetians lost to the Genoese and the Byzantines, the Aragonese destroyed every fleet the French and Agevian Sicily sent against them. At the same time the Sicilians were fighting each other, and the Aragonese were replacing the Bey of Tunis. The Pope calls a crusade against Aragon, which ends up killing the king of France and destroying his army.
AND the whole dispute over Sicily in the first place is an extension of the Ghelf Ghibelline conflict between the Papacy and the house of Staufen.
I know all these threads have to fit together somehow, but I have no idea how these pieces fit. Help?
You need to understand the War of the Sicilian Vespers. This is a very complicated part of history and you are naturally very confused about quite a bit of what is going on. I'll try and sort this out, but to understand this properly, one would need a book, which I'm not going to write. Check out Runciman's history of the Vespers, which really focuses on the run-up to the conflict and not a great deal of the conflict itself.
Setting aside Genoa and Pisa, which is an older conflict, one way you could rope each of these conflicts into a single narrative:
Frederick II dies and the Pope Innocent IV believed that the Regno reverted back to the office and tried to offer it to different lackeys. Yada yada yada, Frederick's illegitimate son Manfred finds himself on the throne, but Alexander IV (we jumped over a pope, but this is complicated and I'm just trying to simplify things for you) is not happy and essentially engineers it through a complicated set of marriage relationships and other bonds that Charles of Anjou should take the crown of Sicily.
Charles invades the Regno and after a short campaign takes over.
Chaos ensues among the nobility of the Regno and Charles and we have the emergence of yet another claimant to the the throne: Conradin. The only thing that you need to know is that he really didn't last.
4.Charles gets the go-ahead to go on Crusade against the Byzantine Empire, which had destroyed the Latin Kingdom of Constantinople, previously established by the 4th Crusade.
A potential crusade costs a lot of money so Charles imposed quite a bit of taxation on the Sicilians and there was tremendous unrest over these heavy taxes and the Angevin troops stationed in the region. Eventually there is a revolt in Parma on Easter Sunday, 1282 when the locals kill a band of Charles's soldiers after they try and feel up some guy's wife.
The Sicilians decide to turn to Aragon and the king to intervene and be the new king.
the Aragonese destroyed every fleet the Angevin Empire sent against them.
All of this is also part of Aragonese expansionism, which includes the replacement of the Bey of Tunis.
AND the whole dispute over Sicily in the first place is an extension of the Ghelf Ghibelline conflict between the Papacy and the house of Staufen.
In a sense yes, but don't think of the Guelf and Ghibellines in terms of Empire and Papacy. Yes, that is the seed of the conflict, but it's much more helpful to think of this in terms of intramural and intraurban factionalis ESPECIALLY in northern Italy.