Alright, going to steal liberally from Artemis on this one, but I can't disagree with the general baseline they've provided. They could use some tweaking though, at least in my opinion. To wit, the following. I make no apologies this time for length, or how the following vote is likely to ramble from speech to factual (ish) narrative.
[X] The World Is Changed - Pt 1
-[X] Before you begin, as much as you dislike the idea of shading the truth (a nicer word for lying) to your own mother, there is her own mind to consider. Simply telling her everything, as she asks, would be beyond her ability to process. You're quite sure of that. She needs time to adjust to the new realities of the world, and you will give her that. With time, you will tell her more, but it will be in her hands when she chooses to ask of specifics. Not yours.
-[X] "Ser Darry took us to Braavos, protected us to the best of his best abilities, then died of sickness three years ago. At that time my magic first awakened, though it was barely more than a few tricks at the time."
-[X] "Fearful of the Usurper's spies and assassins, I vanished into the common folk of the city for most of a month with what little I was able to salvage from the household. My magic made up for the deficiencies of a rather sheltered upbringing there, before I met Ser Richard and another mage newly come to her power. Between the three of us, we were able to gather enough money to purchase a manor within the city." These two points cover our awakening and how the world forced us to take our first steps into the world now that our protector had been stripped away. It shows us rising above our losses, and eventually coming to start anew.
-[X] "From there, I found friends and allies within the city and without. I acclimated quickly to Braavosi life, and began investing to support my endeavours. Magic was returning in many forms, and I chose to involve myself in those matters to protect the less gifted within the city. As well as to hone my strength, and that of my companions. During this time, Dany awakened to her magic too, rather younger than I would have hoped for." Pause for the inevitable eyeroll or otherwise from your sister.
-[X] "In time, I even made a friend among the Keyholders (short explanation of the Drekelis-situation) and dared to reveal myself to the Sealord. I also made my first overtures beyond it, meeting with emissaries from Dorne. One of them, possessed of magic herself, took up residence within the city and in time came to be a valued ally." These two cover our rise through Braavos to the point of friendship with Uthero and our first steps into courtly affairs within the City of Secrets and beyond (Tyene enters the picture).
-[X] Short version of our further adventures regarding Fey, Demons and Vampires. We also became part of Braavos high-society to the point that we won the trust of the Sealord, at least in part." Touch on the Fairwinds and their family, but carefully. That Dany was able to have friends her age that understood her and were 'acceptable to her station' is good. The more supernatural side of the process can be left out somewhat. Broaching the matter of the sentient construct we built to house a human soul is right out. Our peak within Braavos. Connects heavily with the two points before it.
-[X] Leave our death and her deal up to Dany to tell or not, same as her decisions regarding her mental growth. Yeah not even going to touch this.
-[X] End on the note that you had grown important enough to the city that they would have kept you despite Arryn's threats of trade-war, but you decided to strike out on your own. We made the choice to leave, we weren't forced. This is something that she will be happy to hear, even if she might read a little more from it.
-[X] Within the course of your story, begin to lay the groundwork for introducing your mother to the fact that magic, or specifically wisdom in its use, does not necessarily favour noble blood. Many noble lines appear to have found again sparks of magic hidden within their lines, but it comes equally to those without blue blood rushing through their veins. The two best points for this are likely your finding of friends and allies and then again when discussing our entrance into Braavos high-society. Be gentle in this, and careful too. Rhaella will probably be able to guess that there's a reason for you saying so, but leave it alone unless she asks you about it. This is a foundational step, to begin acclimating your mother to what you now passionately believe in. (High or low, bastard or born to a couple in matrimony, the dark forces that you have found yourself pitted against so many times care little. Artificial divisions of blood and heritage are nothing more than cracks in the wall of humanity's defences.) this section in brackets is not to be brought up under any circumstances. It's here as a basis for Viserys' thoughts.
This should cover enough for DP to follow my intentions here. Let me know if you think I've missed anything, though!