Thanks for the translation!
That's some princess. Mu barely asked her to pull some strings to see her mother and whamo! Mother appears instantly! Looking forward to seeing her face when the daughter tells her who the young man she's been looking down on. If she's so worried about her daughter getting in trouble with Anti-Dragon alliance why is she revealing she's a princess in front of a complete stranger? Ten to one Yuan is going to eat most of the food Shuyuan brought and really enjoy it. Probably be hustled into a scene after being mistaken as an extra. Even if Shuyuan was able to hide fact she's a Planet Lord considering how mush Dito are supremacists it wouldn't be surprising if the Dowager sent some troops over to grab the mother and daughter just in case even if doesn't go over herself. Can't be that many centaurs travelling to Pleides who happen to have a daughter with a human.
As for Shuyuan's planet nothing wrong with being into nature up to a point. As long as they have flyers for emergencies and hospitals it's probably healthier there than most cities. Also, Shuyuan doesn't seem like that corrupt planet lord who auctioned off people's deaths where she'd jack the cost of leaving or punish families of those who left. Then again food just doesn't taste the same without all those -icides, hormones, artificial flavors and colors, and preservatives. Although from what the Ningshuang says it seems the nature aspect is being pushed too far. Be nice to see her and Mu debate it but they'll probably be interrupted by the Dowager's thugs.
PS Why is Shuyuan warning her daughter about how much trouble she'll get in if found out she's a princess without making sure no one else can hear her and doing it in front of a stranger (Mu as she doesn't recognize him.) It's like calling out the very secret suppose to protect.