Try tea tree oil lotion or cream for the eczema. Tea tree oil is very good for the skin, it has antibiotic properties to it as well, which makes it also very good for acne. I know people who have eczema that say it works very well. It should be available in your drug store. If not, then health stores would be the next hit.
Praying for you both.
Eczema is such a pesky (is "pesky" too tame a word?) problem, and as far as I know it doesn't go away, although Whitehorse has already mentioned several things that can soothe it. Praying for you and your mother!