I second the rec to use Surcare - me and mine have always had eczema and been allergic to other non-bios like Fairy and especially Persil. Surcare is fine - always an extra rinse and never and fabric conditioner. Always 100% cotton clothes and not too many layers.
Re hydrocortisone - DD1's consultant said better to use a stronger one to get it cleared up, then enable a few days rest, rahter than a weaker one all the time with no break. Also to use until the redness has all gone (so in your case, it might be a near-constant thing).
And never to use at the same time as another cream, as it dilutes it. Leave an hour or so for it to sink in, then put the emollient on.
Another thing to consider if the general moisturisers aren't helping - maybe your daughter is allergic to parabens or petrochemicals? These are found in most creams. DD1 couldn't tolerate any of the creams the GP prescribed when she was a baby. We found Dermasalve baby cream eg here helps as a general moistursier applied 3-4 times a day - absolutely no irritants in that (can be GP prescribed as its darn expensive). It might be worth trying, seeing if the eczema reduces, then you can gradually re-introduce other creams to try to see what might be the irritant/allergen in the other creams.
I would also second what others have said about diet. It is very common for the eczema to be a symptom of a food intolerance/delayed allergy. Its difficult to work through what this might be yourself, but if none of the washing powder/cream recs help, then this really is the only avenue you can go down.