* To replace her real mother: The Other Mother is deeply unhappy and lonely. She sees Coraline as a perfect replacement for her own daughter, who she lost long ago. By making Coraline stay, she can finally have the child she always wanted, and feel less isolated.
* To control and manipulate: The Other Mother is a manipulative and controlling being. She offers Coraline a superficially perfect life, but it's a facade. She wants to keep Coraline trapped and isolated, so she can control her completely.
* To feed her hunger: The Other Mother is a creature who needs to consume life force. She views Coraline as a source of this energy, and wants to keep her trapped so she can drain her.
In essence, the Other Mother's desire for Coraline to stay in her world stems from a combination of loneliness, control, and hunger. Her actions are driven by an unhealthy obsession, and she is ultimately a terrifying and dangerous figure.