The lawsuit alleges among other things that the March fight at Hands of Our Future day care was not an isolated incident.
The plaintiffs are seeking money damages for physical and mental injuries and accuse day care officials, among other things, of assault and battery, false imprisonment, breach of contract and intentional infliction of emotional distress.
Three day care workers who allegedly encouraged and videotaped the fight were criminally charged in August with assault, conspiracy and endangering the welfare of a child.
They are 19-year-old Tiana Harris of Dover, 21-year-old Estefania Myers of Felton and 47-year-old Lisa Parker of Dover.
State officials last month lifted a suspension of the day care's license and allowed it to reopen under probation if it meets certain conditions.