I am almost 30 and have suffered from eczema all my life and to read about the poor kiddies really does break my heart. If you've never had it, as a parent you'll definitely know how difficult it is to cope.
The greasy ointments are best for the dry crusty skin because it stays on there and keeps it all moist (nothing worse than closing your hand and your skin splitting where the joint is on your finger).
I now use DP lotion with 1% hydrocortisone on my face and have done since I was about 11 or 12. This is the only moisturiser I have ever used as everything else just stings. (My mother can't believe how clear my face is now after seeing me grow up with eczema and I still get asked for ID at bars, supermarkets and bottle shops which is consolation for growing up with an adolf hitler patch of eczema under my nose and constant crusty eye.)
My advice to you is to keep it dry, keep it moisturised, get some sun (helps with scarring) and fresh air on it, put your washing through a second rinse, make sure the kids aren't too hot, watch for triggers such as stress (I'm sure teething can be pretty stressful), try and prevent the scratching (infections much? Keep nails short), food elimination and get an allergy test.
Pinetarsol for the bath, Locoid for the scalp (this does sting), hydrocortisone on the bad parts of the face, perhaps a stronger steroid cream like locoid for the other inflamed parts of the body and finally aqueous or emulsifying ointment (the oily greasy thick one - kinda like vaseline which can be used as a soap) on the rest of the face and body as a moisturiser.
Oh and another thing - if kids are rubbing eyes, it could be that they're tired (of course) but they may just have tired itchy eyes which could be a bit of eczema (or hayfever which alot of eczema sufferers also have).
And don't give up, there is a happy medium with eczema, you just have to find it and it will definitely be worth it.
Admittedly, I didn't treat my own skin when I was an infant so am not telling you all how to suck eggs but thought any advice would be helpful.
Good luck!!