Do you share an Island? If so, you should discuss with her before you let Twiggy go. Also, you can close the game before finishing the conversation. When you reload the game, go back to Kabuki to ask him to move in. He will pick another random villager. Do this until he picks someone that you're both okay to let go of.
If you don't share an island, your sister can invite Twiggy to hers when she's in boxes