Awesome story. I really liked this one. More than young, desperate Emma interacting with Emily, which was awesome, there was the idea of Emma knowing what her life would be like, and deciding to 'cheat' in order to improve her life and meet Emily earlier. I loved this line "Emily cringed every time, because maybe she had started out as a wash-out, but Emma, in any time, had never had any scruples about cheating. Time travel was probably cheating. But that just made it more interesting."
I wonder if you could write a sequel/epilogue, either with a young Emily doing the time travel or seeing young Emma back in her timeline, 'cheating'.