Well, this is much better than I expected. It's a shame it's not an ASOIAF fanfic, but you're doing quite well.
I would like to point out that all Valyrian dragons are genetically the same, so there isn't a race of silver dragons, they are silver colored Valyrian dragons and already, the Targaryen themselves have had silver colored dragons before. So it doesn't make sense that they have a low birth rate, unless in your story this family was bent on crossing silver colored dragons.
You literally escaped to the side of your biggest enemies xD, Bravos, if I were them I would attack the MC now that he has only 2 dragons. As for the faceless assassins, I wouldn't worry about that, if they were cheap they would have sent them after the Targaryen heads.
There is mention of obsidian in Skagos, so there may be volcanic activity, you could use that place to settle the dragons.
One question, how many Valyrians did you take with you? Men and women. You need at least a couple of thousand to fill the Island with their race.