AU where Lyanna Stark and Elia Martell swapped roles (i.e. Rhaegar married Lyanna, Elia was betrothed to Robert, Rhaegar abducted Elia for the same reasons)? Would Robert’s Rebellion have played out the same with the North and Dorne swapping places? Would we get Oberyn as Hand, the Starks as secret Targaryen loyalists (Robb in place of Quentyn?), and the Dornish as secessionists (Arianne in place of Robb)?

Interesting question. 

I don’t think a rebellion plays out anywhere near the same. In this scenario, the Starks and Tullys and Arryns aren’t going to rebel, so that leaves just the Baratheons and Martells and they don’t really have the manpower to make a go of it. Maybe if the Lannisters join them, but that’s unlikely to happen at the outset. 

If Southron Ambitions is at all close to true, I see this as a case where the “loyalist” faction takes charge rather than a civil war (especially since Robert’s in the Eyrie when this happens, and also Rhaegar doesn’t really have anywhere to run in this scenario) – Aerys is declared infirm and put into confinement for health reasons, there’s a council of Regents, and a Great Council is summoned to deal with A. who’s on the Iron Throne, given that the king is mad and the Crown Prince technically is an outlaw, and B. what’s the succession going to look like if Rhaegar’s set aside Lyanna for Elia. 

This could get very complicated – the Starks, Tullys, and Arryns are going to express in no uncertain terms that Aegon be chosen over his father as the new Crown Prince, the Martells will seek to defend the rights of Elia’s unborn child but probably would be unwilling to work with Rhaegar’s faction due to the whole abduction thing, the Baratheons would be definitely anti-Martell, as would the Tyrells, and the Lannisters and Greyjoys would be a real wildcard. You’d probably see a pro-Viserys faction develop as a third option between the Aegonites and the Martells.