nah. you got the chicks confused. it was two different broads. one was a stripper (actress: Piper Perabo) Young Joe was fukking. the other was the girl on the farm (actress: Emily Blank). That's why Sara aint know dude. She never met him.
they both happened to have kids the same age who could've been The Rainmaker in the future, so Old Joe tried to kill both kids + the other kid beforehand.
My interpretation of the film is Old Joe killed his older self 30 years ago, went to Shanghai & lived until 2072. In his timeline somehow The Rainmaker lost his mom & started killing all the loopers for revenge of the looper (Joe) who killed his mom as a kid. Old Joe goes back in time. Meets Young Joe. Gets the birth records. Starts finding all the children & killing them
Once he finds the right kid, Young Joe realizes if he lets Old Joe kill Sara, it will start the loop over again as Sid will get away, grow up angry & come back to haunt Young Joe 30 years from now. So Young Joe does the only thing he can do