I'm trying to think of how it's plausible that the Targaryens would have abandoned Dragonstone. They didn't in canon, as they believed wholeheartedly that the Royal Fleet could protect them, as well as all the men on the ships. Furthermore, the Queen was pregnant and would probably have not done well on a ship in her condition. Adding on top of this, Dragonstone was highly defensible, and would have been very difficult to siege, and would be rather well-held by a small force.
When it got sieged in canon, of the 1,000 casualties, the vast majority of them were of the attackers. And that was a pretty small garrison left behind by Stannis who basically took all his men with him, rather than say the Targaryens who'd have all the loyalist remnants left there, and they were nowhere else. With the amount of men the Targs would have had, probably around several thousand, they should have been pretty confident.
And if enough time had passed for them to be worried about Stannis' shipbuilding unlike in canon where they stayed for nine months despite the new fleet being built, then I don't get why Stannis didn't have ships out there to sort of blockade Dragonstone. Instead, he apparently decided to not even bother sending ships up there, when the presence of ships could have prevented the Targaryens from even considering moving out due to the potential for the Royals to be killed by their ship being sunk.
Actually that reminds me, how much time has passed since the war ended or well, since the Targaryens went to Dragonstone? Honestly, it's coming off to me that the Targaryens have escaped with pretty much all their men and stuff as for drama's sake.
Anyway, I like the whole bit with Tywin. Still not keen on Lyanna, considering she went willingly like a stupid bint with Rhaegar in this.
Ok, valid point. But I offer this alternate view:
In canon they had nowhere to run. Sending Viserys and the infant to Braavos on a single ship, as Stannis was closing in, was a hail mary. Besides a few odds and ends, and the personal influence of the Darry knight, they had noone to shield or help them. They might have found a benefactor or two but they knew they wouldn't be safe anywhere.
An the situation in Westeros was different. Dorne yielded just as quickly as in canon, if not slightly faster, but the Reach wasn't alienated by stuffing Stannis and a Florent together. It may be a longshot but having the option open of the most powerful realm, and the sneakiest realm, with the Greyjoys having been oddly quiet...
It wasn't a stretch to think they might get lucky and Robert could catch the pox and croak. Everything crumbles with him, if he dies. Robert could have been a tyrant! He could have stripped half the country of their titles and lands. He could done a whole lot of shit wrong.
But Jon motherfucking Arryn held it all together. In that situation it might be best to adopt a wait and see approach.
Now, however, they got an offer from the Blackfyres - which is dangerous but no more so than the other cousins who have been slaughtering you on the continent - of safe grounds in Pentos. A reasonable one ever where they acknowledge Jon, who they already have
and the three King's Guards they managed to trick into arriving at Pentos - Among which Arthur holy shit Dayne -as their overlord. All they want are marriages and their wealth, influence and arms belong to the Targy's.
Not to mention that on the continent; the Reach is being welcomed, what the shit is the King's brother doing - is that an
arsenal?-, and not even Dorne is calling revenge anymore?
A whole different set of circumstances, in which case sitting pretty in your castle - even if you're four and a half months pregnant-, is suddenly not looking too good.
