Is it possible for prolonged anxiety to cause an enlarged heart and cardiomyopathy in children?

Never. Cardiomyopathy is a condition that can be inherited or it can be produced by a virus or it can be caused by an inherited metabolic problem. It is a chronic disease that affects the heart muscle.
No. Anxiety alone and in the abscense of any other clinical or medical condition shouldn't predispose anybody to have an enlarged heart or cardiomyopathy.