Tokyo Twilight

Tokyo Twilight is a 1957 film directed by Yasujirō Ozu and starring Ineko Arima, Kamatari Fujiwara, Setsuko Hara, Nobuo Nakamura, and Chishu Ryu. It's a family story about 2 sisters and their father who have to make difficult choices in situations where there isn't a right thing to do. This is Often described as Ozu's darkest film, and it is a bleak work without much hope. Family troubles do seem to provide plenty of scope for the exploration of tragedy.

I watched it via Hulu when they offered it free. At this point you need to subscribe to watch it there. There's a trailer at Mubi and a short scene at youtube between one of the sisters and their mother:

DVD Talk says the film is "quite progressive in its honest portrayal of society's normally unspoken secrets" Rotten Tomatoes has a critics score of 100%.