Poor you - its bad enough having it yourself (I do, mildly) but watching your little one with it is a killer.
My DD has it very very mildly and it only comes on if she eats too much dairy. She's fine with the odd bit of cheese/yog/ice cream but if I give her two dairy yoghurts a day it starts creeping in. Controlled by hydrocortisone though as its only small pink patches on her arms.
Mine is worse and my mother (when I was little) and then I (in adulthood) spent my life trying to avoid steroids if we could. Back in the 70s there was no advice about steroids and tiny babies had strong stuff put on their faces (I have little spider veins on my cheeks now as a result!)
But actually the best advice I had recently was that, very delicate skin areas aside, skin thinning isnt an issue. Its better to use the appropriate strength steroid straight away, for two weeks even if it seems to have gone, to blitz the outbreak and control it, and then manage with moisturiser (I recommend Aveeno which DD and I love - find diprobase/oilatum cloggy and itchy) the rest of the time.
I haven't worked it out but I reckon that at the moment I am on two weeks of steroids and then 6 weeks of just moisturiser before the next flare up.
The steroid I need is mometasone (brand name Elocon) which is a step up from Betnovate, which itself is a step up from hydrocortisone. You can go quite a bit stonger than mometasone. It was interesting to see this when the doctor showed me the relative strengths of steroids - I had assumed betnovate was really strong, actually it is second from the bottom!
I also did a York test and found that I am mildly reactive to yeast and lamb, so avoid these as much as poss. I find if I have a lamb roast my exzema is bad the next day. Does your DD have any intolerances/allergies?