Final answer:
The statement by the mother indicating a need for further instruction is her intention to give cough syrup if her child develops a cough, as cough suppressants are not recommended for children with croup.
Step-by-step explanation:
When a nurse reinforces instructions for the care of a child hospitalized with croup, it is important for parents to understand the appropriate home care measures. In the statements provided by the mother of a child with croup, the statement that indicates a need for further instruction is: "I will give my child cough syrup if a cough develops." Cough syrups, particularly cough suppressants, are generally not recommended for young children with croup. Croup is characterized by a barking cough and should not be treated with cough suppressants, as these can interfere with the child's ability to clear mucus from their airway. The other statements about taking the child to a cool location during an attack, giving acetaminophen for fever, and ensuring adequate fluid intake are appropriate measures for managing croup at home.