The story in Marriage Story is far from a happy ending. It delves deep into the problems that a couple can face during a divorce. The characters are constantly at odds, dealing with the aftermath of a relationship that is crumbling. There are no signs of them achieving a state of happiness by the end of the movie. Instead, it shows the reality of how difficult and messy a divorce can be, leaving both parties in a rather desolate state.
In Marriage Story, both characters face a great deal of pain and loss. Their marriage is falling apart, and there are many negative emotions involved. They have to deal with lawyers, custody battles, and their own personal issues. So, happiness is not what they end up with.