Just a lost soul wandering and want to claim the kids as her own and to bring them into her realm.

Nope, the sisters are not dead. They're alive, they're just too isolated. Annabel learns to let go of the past and eventually accept her uncle and his girlfriend and back into real life reality. That's why she says, "Annabel stays.". However, the younger Lily tends to be close to 'Mama'. You can see she always play with her as sort of her own mother and imagination friend. How she smiles every time she sees 'Mama'.

Well, when a person is possessed they tend to do out of this world stuff. Example, The Exorcist.