Researchers are looking for new ways to treat children with hepatoblastoma or rhabdomyosarcoma (RMS) that has relapsed or is refractory: * Hepatoblastoma is a common liver cancer in babies and very young children * RMS is a cancer that starts in muscle cells, often in a child's head and neck, bladder, arms, or legs * Relapsed means the cancer came back after treatment * Refractory means the cancer did not respond (get smaller or go away) to treatment The study treatment HER3-DXd (also known as MK-1022 or patritumab deruxtecan) is an antibody-drug conjugate (ADC). An ADC attaches to a protein on cancer cells and delivers treatment to destroy those cells. The goals of this study are to learn: * About the safety of HER3-DXd in children and if they tolerate it * What happens to HER3-DXd in children's bodies over time * If children who receive HER3-DXd have the cancer get smaller or go away