In the future, Serena is Neo-Queen Serenity, ruler of the thirtieth-century, Crystal Tokyo. Darien is King Endymion, and Rini is their future daughter, Small Lady. Because the life span of the people who live on the Moon is around 1,000 years, they stop maturing around 22 years of age. Neo-Queen Serenity has Rini at 22, and stops maturing, which would explain why she still looks exactly like Serena. (hence them being the same person -_-;) Because Serena and the others are technically living in the past, with the villains attacking them, it's affecting the future.
The Dark Moon Family are a "family" on a planet on the edge of the galaxy, called Dark Nemesis. It is inhabited by people of Earth who did not want to be cleansed by the silver crystal (they had to be for Crystal Tokyo, meant as a utopia, to be formed)
One day they attacked Crystal Tokyo, and the Queen was outside the palace during the battle. As a bolt of energy was aimed at her, the four scouts protected her, and encased her in a crystal. For some unknown reason, she was put into a deep sleep. When the scouts beat the enemies in the present and Rini is returned home, Neo-Queen Serenity is awake.
...I know that seems rather confusing, and if so, I'll try to straighten it out. In one episode, all the inner scouts go after Rini, who left using her Crystal Key. A hologram of King Endymion appears, and continues to tell them the current status of Crystal Tokyo (the future). In turn, the scouts defeat the enemies in the present, thus making the battle in the future impossible, which then causes Neo-Queen Serenity to wake up, and King Endymion to heal (he was hurt in the attack, hence the hologram projection of himself).