All three of my children have a mild case of eczema. They are 10 yrs. old, 4 yrs. old and a 10 month old. For my older two children their doctor had prescribed a mixture of Aquaphor (1-1) and TAC 0.1% (Triamcinolone) 4oz., ask your children's doctor. It worked wonders for them. They use Lubriderm lotion twice a day. When they get an outbreak, I put this medicine on and it clears it quickly.
Several years ago I took care of my nieces, when my sister went deployed, and they had a severe case of eczema. Their skin was broken and bleeding in some areas. This causes other problems, being young and like all other children love playing outside, etc. They were an easy target for acquiring an infection.
I took them to a Dermetologist and the best way to help them, was by putting vaseline. I did this for several weeks and it did wonders for them with such a severe case. After their skin healed a bit, I started on the Lubriderm, two to three times a day. Before my sister came to pick them up they looked like they never had a severe case at all. The Dermetologist also recommended, moisturize, moisturize and never let it get to a severe stage, because then it is harder to get their skin back to normal. It's a longer process. At times, depending on the severity you would have to moisturize the skin more than two or three times a day. With my children I still have them moisturize twice a day, even thow they don't have an outbreak as of now.
Also eczema is worst in winter, avoid wool clothing, use cotton so skin can breath. They told me not to use sheets for the dryer, because the strands on the sheets sometimes come off and stay on the cloths. Some docs told me to change detergent, others no (I never did). Use dove soap, unscented. If u bath them everyday, bath them every other day. In between wipe them down on their diaper area, around mouth and neck. Bath them in cooler water, not so warm.
Tell their doctor how long they have had it for. Use vaseline for now. Can't wait for them to get better soon. If I remember anything else, I'll write again.
Updated
When your done with your childs bath, do not dry your child completely, apply lotion with semi wet skin.