Bleach baths are an important component of this twice a week 1/2 cup of household bleach in a full tub of water. It sounds irritating but it's like a swimming pool and diluted enough that it shouldn't cause harm even with children with eczema. It's actually a common recommendation for kids with eczema to reduce their risk of skin infection. Ensure you are washing your towels in hot water to kill bacteria that could grow on them and consider using paper towel in the bathroom rather than hand towels. Staph bacteria can easily spread between close household contacts so make sure everyone is on the same page so it doesn't continue to spread.