I hope that Roose and Walda's child will become lord or lady of the Dreadfort but you never know. Still if Roose losses he has kind of lost his rights by going against his liege so it will be up to the Starks or Stannis to decide what will happen with it.
If Stannis had gotten hold of the Targaryen kids they would die. Just like Rhaegar's children they were potential dangers to the Baratheon dynasty and if Daenerys returns triumphant with her dragons then it would rather clearly illustrate the danger of not having them killed.
Well to be honest this kind of situation was kind of something which the prince shouldn't have been handeling himself; its bad enough that the Darklyns have the king and if they got the crown prince as well?
However given that Tywin was sitting outside Duskendale and that Rhaegar was not the guy who went around itching for a fight it seems to me that he would be in King's Landing and potentially he was helping to deal with day-to-day affairs of running the realm. Rhaegar's big mistake was of course that he didn't get real-action experience before the rebellion by being present at Duskendale or hunting down the Kingswood Brotherhood. Although foreseeing the kind of developments that lead to the rebellion is most likely difficult.
I would say that the Lannisters can probably raise more men from their own lands. This is based on the fact that no other House seems to have been, until recently. been awarded the lands of the Tarbecks and the Reynes and so I would think that these holdings went straight to House Lannister. Hence why the Lannisters are probably the strongest Great House if we discount the bannermen.