No child deserves abuse, no matter how "troubled" or "difficult". Children internalise abusive messages because of an unconscious need to maintain attachment to the abusive caregiver. Abusive people blame the child, usually like "if you aren't so difficult, I wouldn't have to punish you."
From one survivor to another, I recommend Beverly Engel's book "it wasn't your fault". She's a therapist treating abuse and a survivor herself.
If you're working with a therapist or looking for one, or just want to know what abuse healing can be like, Gretchen L. Schmelzer's book "Journey Through Trauma: A Trail Guide to the 5-Phase Cycle of Healing Repeated Trauma" can be very encouraging and validating.
Another very helpful and informative book is "Complex PTSD: From Surviving to Thriving" by Pete Walker.
Wishing you healing. [emoji173]