Lotte Lockwood, 21, of the unit block of Chelwynne Road in New Castle, was arrested after the incident on Wednesday evening.
New Castle County Police say it was around 6:30 p.m. when her child, who is just shy of three years old, was found wandering near New Castle Avenue.
Officers soon learned where the child lived and, upon entering the home, found that two other children - a one-year-old and four-year-old - were in the care of Lockwood's father.
Police say her father, a 55-year-old man, was incapable of caring for the children, saying he was "found lying on the couch and, due to his medical condition, could not remove himself from the sofa without assistance."
In addition, police say the home was filled with so much trash and clutter that it was difficult to move around.
Lockwood arrived at the home about 15 minutes later, police said. She allegedly told them she had left the house at 5:30 p.m. and went to a store, then a friend's house. She came back after getting a call from a neighbor that police were at the house.
The children were placed with another family member, police said.
The father was taken to the hospital to be evaluated and to be treated for previous medical conditions.
Lockwood was charged with three counts of endangering the welfare of a child. She was arraigned and committed to the Delores J. Baylor Women's Correctional Institute after failing to post $600 secured bond.