I think one problem with your PLO comparison is that Palestine is occupied directly by the metropolitan power(Israel), and hence the PLO spends most of its time and energy battling that country.
Whereas the US hasn't really occupied countries in Latin America for some time now, but rather exerts its influence via proxy armies(eg. the contras), client dictatorships(eg. Pinochet) etc, with only the occsassioal direct invasion(eg. Panama). Thus, the US itself is usually not targetted by the local resistance movements, but rather lets its proxies take the wrath.
As for Al Qaeda, it seems to me that a distinguishing thing about the group(assuming it really exists, which is another debate) is its religious, as opposed to ethnic or class, identity, ie. it takes its stance on any issue depending on what side Sunni Muslims are on.
Boston Irish might have sent money to the IRA, but didn't really bother supporting the FLQ in Quebec, even though the FLQ also claimed to be fighting on behalf of a Catholic population. But Al Qaeda(again, assuming it's a real thing) seems willing to take up the cause of any Sunni population claiming oppression from the infidels, and will even on occassion align with imperial powers, if those powers happen to be fighting the enemies of the Sunni(hence, ISIS fighters being on the same side as American-backed militias against the Alawite Assads).
So, to get a Latin American Al Qaeda going...
Maybe find a way to fuse populist economics and anti-colonialist analysis, on the one hand, with right-wing millenarian Catholicism on the other. The resulting group would glorify the devout peasantry, villify the land-owning aristocracy and secular-ish military governments as heretical, and stage miitary campaigns against the latter two, AND their American benefactors.
Basically, Oscar Romero meets
Bill O'Donohue, with a bit of homicidal mania thrown into the mix. Unlike the Latin American leftists of OTL, this group would eschew contact with left-wingers in the British Caribbean(buncha damned prots) and people like Fidel Castro and the Sandinistas(for obvious reasons). They might even strike up the occassional ad hoc alliance with the US against the infidel Comunists.
Thelogically, the group would be heavy on the Marianism. All Mary, All The Time.