Connie was one of Rat's various dates, but unlike them she was a serious control freak.
Now, as described above, Connie is a control freak. She has a strict schedule, so even if you sneeze she tells you, "Your last _____ was not on our schedule." She even forces you to have new friends and family. Hence, Rat dumped her, and Pig began dating her, then later dumped her.