Final answer:
To prevent the transmission of roseola to siblings and other household members, the child should not share drinking glasses or eating utensils, as the virus is transmitted through saliva.
Step-by-step explanation:
The nurse should advise the mother to avoid allowing the children to share drinking glasses or eating utensils because roseola is transmitted through saliva. This viral infection is common in children and is primarily spread via direct contact with saliva or respiratory secretions. Other preventive measures include practicing good hand hygiene, not sharing personal items, and covering the mouth and nose when sneezing or coughing to prevent the spread of viruses like roseola.