My DCs all suffered from eczema from time to time since they were babies. We have a family history of eczema, it runs in our blood. Eliminate all perfumed products from their bath and skincare products. Be really vigilant if the product contains essential oils because a lot of them are known to be skin-sensitising (yes, just because its natural doesn't mean its always good for you!) It will also help you a lot to learn to read ingredients lists for products so that you know exactly what's inside. You can often try Googling for more information about each ingredient. Some preservatives are skin-sensitising, like Linalool, Geraniol, etc. There is a list of all the 26 allergens commonly found in skincare and bath products here that were documented in EU directives for their skin-sensitising/allergenic properties : ec.europa.eu/health/ph_risk/committees/04_sccp/docs/sccp_q_196.pdf
I've found that its quite difficult to avoid all of the potentially allergenic ingredients in commercially available products, but if you know what's inside the product, then you can try to pin-point the possible causes when your DCs have an eczema flare-up after using them.
Products with strong detergents in them strip skin of oils and aggravates eczema... There has been a lot said about SLSs (Sodium Lauryl Sulfates) and SLESs which you can google... however there is another camp which claims that SLESs are actually quite gentle... Cocamidopropyl Betaine has been listed as a possibly allergenic ingredient though its quite often used in baby products because its supposed to be gentler than SLS. EWG's Cosmetic Database claims to be an info-portal informing the general public about what's really harmful in commercial skincare products (www.ewg.org/bodyburden/consumerproducts) but because of its involvement in environmental lobbying groups and its database is always touting some enviro-friendly organic product as the next best thing (when it isn't always the case for eczema sufferers) means I don't always take it as the gospel for researching ingredients. Paula Begoun's Cosmetics Cop Ingredient Dictionary website also claims to offer consumers information on cosmetic ingredients (www.cosmeticscop.com/cosmetic-ingredient-dictionary/A.aspx) ... I do tend to listen to her more though... based on my own experiences.
Also, warmer weather tends to aggravate eczema or trigger flare-ups in my family. And hayfever... To make things more confusing, my DCs could show an allergic reaction to a certain product a year ago, then take to the product fine another year! We have tried many products over the years and I cannot say for a fact which ones we are truly allergic to... let's just say, it changes. And hydrocortisone and other topical corticosteroids like that are great for flare-ups but not advisable to use them for long term - they thin the skin slowly through continuous usage and eventually cause skin damage amongst other negative side effects. If you find you have to rely on these creams long-term to keep the rash in control, it might be best to look into other ways to try and treat/prevent this condition, i.e. diet and changing the skincare products for eg. Whenever skin starts to flare up with eczema or hives all of a sudden, examine the foods you've eaten very recently (within the past day or two) and the weather, and whether you've recently changed products, etc. I find for myself, eating peanut products makes my skin more prone to rashes. I don't go into anaphylactic shock, but I definitely have some kind of skin reaction to eating peanut products, so I try to avoid it, or just eat sparingly and then I will often be fine. And also insect bites can cause allergic skin reactions too, more so with eczema prone skin, so when there's gonna be lots of insects buzzing around, it might be worth using an insect repellant (though that too can be a tricky issue - working out if the ingredients in the repellant might be allergenic to your daughter!) And suncream...a lot of the commercial ones are potentially skin-sensitising for eczema sufferers.
So basically, know your ingredients, and you'll be much better prepared to tackle this eczema head on! :)