This movie had an amazing realism

The acting was so good that for all intents and purposes the actors were invisible -- they WERE the characters. The plot was, as you mentioned, largely a series of minor events. There were major events common to family dramas -- the bigamy trial, the children concerned over their inheritence, the pregnancy, the resulting fights, and so forth.

What the trivial events do is to create the characters and their relationships. In a more traditional screenplay, you say "Oh, that's character development" or "oh, that's a plot twist." That was completely absent -- it was just life going by. And it did all the things that more conventional plots do, but completely unobtrusively.