The End (spoiler)
*Spoilers below*
One of two things happened here.
The first possibility is that the Emily Clone was able to monitor where she sent Emily Prime, saw that she screwed it up by sending her "hundreds of thousands of years into the past", and corrected her mistake.
The more likely, and more grim, is that Emily Prime died when the "extremely dangerous time travel" dropped her into the past and left her there. Because Emily Prime died, the subsequent Emily clones never existed, and Emily 3rd Generation never transported Emily Prime to the future, nor sent her to the past, therefore adjusting the time/space continuum and leaving her in the present, exactly where she started.