If being warm is a problem then keeping cool is best for those infants.
we used some eczema suits but had to cut a hole in fold over mittons so he could suck his thumb for comfort. was very useful when child had chicken pox and eczema flare up!
most children outgrow this severe form of eczema by five, and often improves or changes depending on time of year and state of health. (atopic march)
I would ask for environmental blood tests to look for causes, but even so this doesnt always work for some.
I would change creams/prescriptions from gp until you find something that works, and keep up a soild eczema treatment plan. For instance all over body moisterisation about five times a day.
Hygeine is important, as its easy for skin to become infected and lead to greater strength of steriod creams and antibiotics. low percentage creams do help if correctly given.
I would personally not bother with alternative therapys if you suspect that food may be an issue or environmental allergies.
have to say that I personally dont think that homepathy works, and would never recommend it.
I think the ezcema society charity would be my first port of call for advice, and perhaps contacts for recomended clothing.