I Am A Child Of This House

Story:

Pink Ice was able to lead a relatively normal life, except that, first, she remembered her past life and, second, she was the illegitimate daughter of the only Duke of the Empire. One day, when the main character turned 11, her prostitute mother decided to show her to her father and demand money for her maintenance. Our only Duke instead just bought back the Pink Ice for 20,000 gold. How will her life change now? What awaits her next?