Another example is Millie's mother, who gave her alcohol as a young child to "help with naps."
Spring Awakening has Martha and Ilse, who both suffer from this sort of abuse. The song "The Dark I Know Well" is all about sexual abuse.
In Electra, Clytemnestra and Aegisthus verbally abuse Electra, confine her to the house, prevent her from marrying, and leave her in neglect. This crosses over into physical abuse with their plan to seal her up in a cave to die.
Sweeney Todd: The Demon Barber of Fleet Street has Adolfo Pirelli, who is physically abusive toward his ward Tobias Ragg. According to Toby, Pirelli is "a good one with the lashings", and his treatment of the boy during the street scene is deplorable. This sets Pirelli up quite nicely as an Asshole Victim even before The Reveal of his past with Sweeney and his attempt to blackmail him.
In Wicked, Elphaba's adoptive father is emotionally abusive, due to favouring Nessarose over Elphaba.
In Les MisÚrables, the Thenardiers are this to Cosette, who they are in charge of while Fantine works and sends them money to care for her. Instead of looking after her, they beat her, dress her in rags, leave her in the cold, and force her to do all their chores. Their own daughter, Eponine, is treated like a princess as a child. When she's a teenager and actually in her father's gang though, she's treated far more roughly by him. Most notable is the scene in which Thenardier and his gang try to rob Valjean's house, and Eponine screams to warn them. Thenardier threatens her for that and, in many productions, slaps her to shut her up. In the full version of "Beggars at the Feast", both the Thenardiers are horribly dismissive when Marius sadly tells them how Eponine is now dead.
Buried Child has Dodge and Halie. Both emotionally abuse their sons onstage. Prior to the events of the play, Halie has sex with Tilden producing a baby which Dodge drowns.
In Heathers, Big Bud Dean, J.D.'s father, is emotionally abusive to his son, makes some very unsettling comments about his son's girlfriend, apparently drove his wife to suicide, and is constantly drunk. Physical abuse is also heavily implied.