Without knowing any specifics about the deck she's running it's almost impossible to give meaningful advice.
But, bear in mind the deluxe sets were also designed for a metagame in which all of the chapter packs were part of the card pool. In a more limited setting, sometimes certain builds do crop up that would be above the curve.
Horn of Dragons, Frozen Moat, and a couple of others are cards which can ruin a Dragon deck but that you just don't have. Also hard to say without knowing the build you're trying against it.
Lastly, it seems like you're playing it at home just against each other--it's hard to know whether there might be some rules oversight that you might be laboring under, or some answer you just haven't been exposed to. Are you hitting them with Valar Morghulis? Dragon decks lose a lot of oomph if you can kill Rhaegal or Daenerys.

At the start of the game, you look at the top 4 objectives of your objective deck, and pick three to open with. Say I have 6 Sith objective sets, and 4 Imperial Navy objective sets.
 
I have about a 7% chance to open with no Imperial Navy objectives to choose from, but less than one-half of 1% chance of opening with none of my Sith objectives available. With a 7/3 split, there's a 17% chance I open with no Navy objectives, and zero chance I'll have no Sith objectives. And with an 8/2, it's a 33% chance that I have no Navy objectives in my opening selection.
 
Since the affiliation card provides a resource that is always available, playing the card of the splashed affiliation means I'll always be able to play my cards of that affiliation.