One major gripe I have with the Targaryens in the game is the selection of characters: I just can't relate to all the strange names, all the guys and girls that - in the books - tried to betray Dany (or did so succesfully), but are supposed to be backbones of the Targaryen strength in the game. And with the events in Dance with Dragons that becomes even clearer: I don't think the Meereenese should be Targaryen faction (and the Yunkai'i even less so), but neutral.
On the other hand I would really like to see some of the supporters of the Targaryens in Westeros: Why not make a house Darry subtheme (with Willem Darry as a great card that saves nobles, or something like that), why not turn to the memories-sections in the books and give us Old Owen Merryweather, young Jon Connington, a few Tragaryen Kingsguards, a Targaryen Varys, and maybe even Mad King Aerys. I'd like cards of this recent period of history much better than legends like Balerion the Black and Daemon Blackfyre.
Maybe we'll get a Targaryen Golden Company now...