Marilyn Kay Edge, 42, of Scottsdale was arrested Saturday after police said they found the bodies of her 13-year-old son Jaelen and 10-year-old daughter Faith in a Santa Ana, Calif., hotel room.
The manner in which the children died was not reported.
Police learned of the children's deaths after Edge allegedly tried to commit suicide by driving into an electrical box behind a home improvement store in Costa Mesa, Calif.
Edge appeared before a judge Tuesday by video from the Central Jail in Santa Ana to arrange for an arraignment date, KTLA-TV, Los Angeles, reported.
When the judge asked Edge about setting a date, she twice responded, "only if you promise me the death penalty."
Edge's arraignment was scheduled for Oct. 25, and the prosecutor said the death penalty would be "assessed at the appropriate time."
"The only death penalty she's been able to achieve successfully has been that of her children," Senior Deputy District Attorney Sonia Balleste said.