Alright. So. You're... aware of how people can be from the same world, but different times here.
The Stark sisters and Jon Snow are both from... a little further in time than you are. The reason for the distrust from some people is that after the death of your friend... there's no nice way to say this... you snapped. You had Drogon torch King's Landing and everyone in it.
I've spoken with Lord Snow, and we are in agreement that being here, along with our influence, will be enough to prevent something similar from happening here.
Once we can show the Starks that you are not a threat, and that you only want to rule Dragonstone, I truly believe things can be smoothed out, and that a cordial, peaceful coexistence can happen.
Basically, Khaleesi? We need to make them see the caring, kind woman that I see every day.