In order to get Ami to move in you have to own the Manor and purchase the extra rooms upgrade. Then, if you completed the Morgana quest you can return to Ami's room and ask her to move in with you.
When you finished the murder mystery you were given three choices about the fate of Ami.
One where you bring her home with you.
One where she stays as Morgana's punching bag.
And the other one that you have no reason to pick.
You can only bring her home if you picked the first one (rescue) but if you chose (recycle) she can't be brought home.
At least you got money, I suppose.