If I remember correctly I watched a Chinese drama a few years ago where the FL's dream was to become the best wife and mother of her children she could be and worked and studied hard, but at the same time got a lot of criticism from so called "modern" or "feminist" women who wanted her to focus on a career and becoming economically independent. 

Also I think I saw a similar Japanese or Chinese drama but where it was the reverse and it was the ML that focused all his energy on becoming the best father and husband, I think he even learned martial arts etc so that he had the ability to protect his wife and children. 

Anyways, I'm not looking for the exact titles, as my memory might be a bit confused, but I'm looking for something similar, where the leads focus is on their family rather than career or money. 

That sounds exactly like Totsuzen Desu ga, Ashita Kekkon Shimasu. Basically the same story as the chinese drama you watched.

If you have not seen it, this is the most fitting one ;) 

Interesting concept, I'd like to see this and similar series.

maybe Gibo to Musume no Blues, though this is mostly about choosing to be a mother, the FL literally resigned from the job where she excels and is in demand to be a mother and wife

  • Gokushufudou (it's the ML who focuses on the family)