Would you pls suggest me dramas where FL is similar to Chu Qiao ?

1. She is matue , smart and kindhearted girl

2. she only shows her soft side to her family members 

3. Most important: she's doesn't need Any man to save even after romance begins 

Try Noble Aspirations.

There are a few female characters like that but the main one is Bi Yao

Of course Hig Goddess  Bai Jian from Tree Miles of Peach Blossoms. 

Wei Ying luo from the story of yanxi palace 

Empress of China

Princess Silver

Legend Of Yun Xi

Princess Weiyoung

Empress Ki (Korean but very very good)

Legend of Mi Yue

Rise of the Phoenixes (on netflix)

Ruyi's royal love