Sorry, did not read before posting.
OK, we need to talk about eczema. Again. Please use the search to look up eczema, or use Google to look up "Soapmaking forum/eczema."
First off, eczema does not have any magical cure. However, if you take away the cause, then you get less(or no) more eczema. So, the idea is to remove potential causes FIRST.
Start with soap, yes. Quite often people find that their eczema is minimized in the extreme JUST by switching to a true soap, and away from the synthetic detergents in most commercial soap. Mine is completely gone now. The soap is not the cure, though. It is simply taking away the trigger.
Secondly, though, you need to look at laundry detergent and/or dryer sheets. You need to(and everyone else) switch to either "free and clear" products, or make your own soap and skip the fabric softeners.
Then, if that does not work, you have to go to a doctor and figure out what is causing the eczema.
Now, for what kind of soap you are looking to make, I would avoid all fragrances until everyone is eczema free. I would also avoid high coconut oil soaps-stay with 15% or less. I LOVE my lard soaps for how conditioning they are. This is my (current) favorite recipe:
Lard 80%
Coconut Oil 15%
Castor Oil 5%
Superfat 5-8%(5% for summer, 8% for winter)
If your nose is sensitive, though, you could go more to this:
Lard 55%
Olive 25%
Coconut Oil 20%
Castor Oil 5%
Superfat 5-8%