Was the idea of a regency for Aegon VI and Rhaenys ever really explored by the rebel faction? Rhaegar may have been more agreeable to a surrender if he knew his children would succeed him, and it was possible for him to take the black. Or did Robert just really want the throne that badly?

No, the idea was not explored, because the Rebel Alliance acclaimed Robert as their king – note the order of operations there – and once you’ve crossed that particular Rubicon, there is no alternative to removing House Targaryen altogether.

And I should emphasize, because I’ve responded to a few of these, but the political logics of a lot of these alternate scenarios are not sound. Even if Rhaegar was willing to take the black (unlikely), and Rhaegar’s supporters would accept that (unlikely), it’s not a good idea for the Rebel Alliance to support a regency for Aegon VI, because infant kings grow up and have excellent motives to revenge themselves against the people who overthrew their fathers.  

Hey I loved your “Politics of the Westerlands” series. Had Aerys died at Duskendale do you think Tywin would have succeeded in wedding Rhaegar to Cersei? If so how would it have affected the politics of Westeros? The Southern Ambitions?

Good question!

I think the politics would have been quite complicated – on the one hand, Tywin has been Hand for 15 years, he represents stability and competency in government, he’s the Crown’s major creditor, he’s got the army in hand de facto. It would be rather difficult for Rhaegar to refuse him in the moment.

On the other hand, Tywin’s power is in Rhaegar’s powers to dispose of, simply by naming someone else as Hand. (Indeed, if Rhaegar is really Machiavellian, he could publicly blame Tywin for causing Aerys’ death and really go to town on him.) 

On a third hand, it’s not clear how many alternatives to Cersei there were at the time…there’s no Arryns, 

In terms of the political effects…there are going to be quite a few Aerys loyalists who will run a rumor campaign that blame Tywin and Rhaegar for killing Aerys. I don’t think it’ll be given much credence by most (Rhaegar was quite popular among the smallfolk)…until something goes wrong and then people will start to whisper. 

There’s definitely going to be tension between Tywin’s faction and Rhaegar’s faction (Connington, Lonmouth, Mooton, the Daynes and the Whents) over access to offices. Rhaegar’s going to want his own men around him, and Tywin’s going to want jobs for Tygett and Gerion and Kevan and Illyn Payne and the like. And I would argue this tension would expand as other Houses get tired of Tywin’s monopoly on royal power – the Tyrells, the Martells, the Southron Ambitions bloc, these folks want their fair share of honors and offices and if they feel like A. Tywin’s never going to leave and B. he won’t share, you’re going to get some “evil councilors” politics brewing fast.