Left with light blotches all over arms, is this normal?

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yes this is from the eczema i experience the same thing. once the eczema is gone the pigmentation will go back to normal eventually with time. For me it seemed like it took a decent while but pigment does all even out. 

Now if your treating your daughter currently for ezcema thats what you should be more focused on, the current treatment for doctors is to presribe some kind of steriod cream problem with that is it just temporarily makes the ezcema go away then comes back forcing you to contantly be applying the steriod cream eventually you get something called steriod addiction. Just look at some of my other post and comments to read more about it. 

my best advice on what completely cleared me up is dont apply nothing to the skin, you will have good days it might get worse then get better then all the sudden seem like getting worse but eventually eczema will just die out of the body with just time and time alone. Since your daughter is still young this is the best time for her to heal, if you have her on any steriod creams or that nature stop them asap. if you do have her on them, yes she will flare up the ezcema will get worse but since shes young eventually with time it will just die out of her body, since shes young it shouldnt take that long and by not long probably half a year maybe more, 

for me i started steriod creams for ezcema at 18 used them all the was to 27, i finally did enough research and realized its the creams that kept prolonging the ezcema, i finally stopped all steriod creams. It took me a full 2 years of drastic flare ups, burning skin pigment loss but i can finally say its all gone, not one single rash not one single flare up or anything ive completley healed. 

If your not treating her right now with anything then goood just keep it that way since shes young her body will eventually just burn off the ezcema it will go away i promise. Everyone here might say try this soap or this lotion or this and that, none of that works all it does is disguise the sympton then as soon as u stop any of those products the ezcema or rash or whatever just returns. I know most ppl dont want to accept this answer but the best answer is just time, let the body do its course and it will balance out i promise.