Can someone recommends drama :

1. historical Chinese

2. about more or less "typical family"

3. big politics is a background at most.

Love Like the Galaxy is based on a novel whose author also wrote the original novel for Story of Minglan. It's the only historical drama that has reminded me of Minglan with the family dynamic and a smart underdog female lead. It is much less realistic though and the romance is more immature. Still a great drama, I recommend it! 

If you're open to modern dramas, All is Well and The Bond are also excellent dramas where family is the focal point.