The Suspicious Housekeeper (2013)

It's the original Japanese drama.

Both include a broken slightly messed up family.

Both have slightly pathetic adults.

Both include an unconventional outsider. A tutor in Kazoku Game and a Housekeeper in The Suspicious Housekeeper.

Both have very good character developement.

(Please note that the suspicious housekeeper is a korean drama)

I would say when i first watched the suspicious housekeeper, the housekeeper reminds me of the teacher in the queen's classroom. They don't smile, they kept hiding their feelings, that's why people tend to misunderstood a lot, make people around them uncomfortable at first but then when they realize their true nature, they came to like them, they have a reason why they act that way, it seems that both of their son died.

Both about families with serious problems and broken bonds that someone comes to help them reconstruct their relationships and become a real family again.

This is the original, Japanese version. It has the same plot but this was shorter.

Both revolves around people who choose to be the best at housekeeping after their personal life is ruined.

They're not really alike but give me the same heartwarming feeling. Both are family dramas - though this one isn't as heavy as Angry Mom - with great acting and realistic problems with unrealistic behavior (which makes it funny).