Final answer:
The nurse should suggest performing the assessment while the mother hugs the child on her lap to provide comfort and calming support.
Step-by-step explanation:
The most appropriate response by the nurse when a child is admitted to the hospital with pneumonia and the mother asks if it would be better for her to leave the room is, "I can perform the assessment while you hug the child on your lap." This approach can provide comfort to the child and potentially make the assessment easier, as the presence of a parent often helps to calm an upset child. It is vital to maintain a supportive environment for the child during medical assessments, especially when they are feeling unwell and scared.