I was just wondering if the eczema came straight back when you stopped steroids.

To me the fact it comes back means there’s something there 'causing' it to come back.
My little boy had a little patch on his face, I just couldn't clear it. I'd use steroids.... it would settle. Then come straight back.
I noticed when it got red - he'd been in our dinning room.
I then worked out; it was when he'd been playing/chewing some old toys of mine. I washed these toys in soap, and the patch went and never returned.
The toys when I'd got them out of the loft 8 months earlier had been washed in fairy liquid
With regard to the detergent thing, I've been helping a couple of friends locally to go detergent free. I'd never under estimate the effect that detergents can have on these sensitive little children’s skin.
1 parent (whose little girls eczema was just behind her knees) like me got some new organic bits and bobs and hand washed them. None of her little girl’s clothes go into the washing machine and she uses natural cream..... The change in her little girl’s skin is amazing, like Josh she's free of eczema and other than a little flare now and then it is great.
The other parent is still using the washing machine and old clothing, there road is way more rocky and although they are seeing big improvements they get set backs all the time. It's hard to see the progress they are making often as one item of clothing can set her skin way back again, and the patches do not get the time to heal properly.
If you decide to go detergent free, I'd really advise to try and 'test' your daughters clothing first. Going detergent free can be amazing and have unbelievable results but you have to be so meticulous that it's hard to notice the effects doing it 1/2 and 1/2 in fact a mixture of detergents and soap can in fact be more irritating to the skin than just soap.
I really must spend time writing up a page on this properly

I just want to say, if you want to try 'detergent free' and I'd strongly advise it to any parent of a baby with eczema - do a test first.
Get a couple of new clothing items that cover the babies body, organic may be better but any new clothing is better than an item that you have washed.
Then let your child ware only those items for at least 1 week. Wash one ware one, and wash it only in very hot water in a sink washed out with 'true' soap first. (All by hand, no washing machine rinse or spin and no tumble dry) With in the week the skin should be settling down.
This should give you an idea of how the detergents are affecting the skin

If you see an improvement then you will need to start ridding your home of detergents, but just 'using' soap flakes unfortunately won't give you much of idea as to if it will help or not.