Don't know what to tell you about the dragons, specifically. Whatever makes sense? There's lots of room for what makes sense in case of dark age kinship, is all.
Maybe you band up your supporters and say that thing that used to be a dutchy? - well it's a kingdom now. Maybe your older sibling steps down and gets carted off to a monastery somewhere, and so you become king or queen. Maybe whoever the other major players are in the kingdom decide that they want to calculate who's the most royal by a different genealogical system, and so you're royal now. Or maybe some sort of weird change comes about and you institute a royal diarchy, where there are two kings or queens instead of one. Or maybe you crown yourself king by right of conquest.
The thing to note that medieval politics are a bit of a mess. In Game of Thrones terms, Geoffrey, Stannis, Rob, Renly and Daenerys are all Rank 1. Which is a messy but understandable (and replicable) situation, right?