The phrase "unfit mother" refers to a mother who is considered to be incapable or lacking in the ability to properly care for or raise her child. Full definition
The eponymously named «Sheep» (a nickname presumably owing to his easily swayed nature) is first glimpsed nervously pacing a courtyard beyond a carefully framed window pane, his destiny debated in a foregrounded bit of exposition that sees his alcoholically unfit mother losing legal custody of the boy, in spite of her professed love. (parallax-view.org)
Eventually the New York tale of a flummoxed, possibly unfit mother (Mila Kunis) converges with a superstar painter (James Franco), the father of her child. (shepherdexpress.com)
Although English actress Imogen Poots isn't American either, she nearly saves the exercise by bringing a shred of human warmth to her portrayal of a flagrantly unfit mother who drags her 8 - year - old son through a host of illegal schemes in a desperate effort to put a roof over their heads. (variety.com)