A mother with severe, delusional depressive illness, believing she has passed an incurable inherited curse on to her children that guarantees them a life of suffering, kills both her children and then attempts to take her own life, describing this afterward, within her belief system, as an act of protecting them. What is this pattern called?

This is extended suicide: the killing of a loved one, driven by a delusional belief system (here, a hereditary-curse delusion) and understood within that delusional framework as protection rather than harm, followed by an attempt at the person's own suicide — exactly the pattern the phenomenon's own text describes. It is not an impulsive act of violence, since this is driven by a sustained, specific delusional belief rather than arising without identifiable motive. It is not ordinary child homicide, since the underlying motivational structure here is delusional mercy, not hostility or an unrelated motive. And no loss of memory or sense of self is described, so this is not a dissociative episode.