I dont know alot about villager trading, but Tutu moved into the spot JUST as i was planning to build a house there. Anyone who wants her can take her if you know how!
You have to wait or TT (time travel) until she asks you whether she can move out. Then, the day that she is in boxes (when she is locked into her house with her furniture inside boxes) you can invite a mayor to your town and they can invite her to move in to their town.
If you want to get rid of her quickly I suggest TTing.