Ok. Usually I don't post here about eczema because people give you shit advice and get cross when I mention aspects.
DD had eczema very early, prior to 12 months. It got bad mostly in her wrists and hands until her skin cracked and it thickened so we managed a referral to see Adam Fox and one of his nurses talked me though what to do in detail.
So as their immune system is fighting off the eczema they will run hot - make sure they don't get overheated especially in bed. Sleep in pants when it's warm and not heavy duvets etc. make sure nothing is stored under the bed so you can hoover under it.
You should give them a bath daily but for no longer than 10 mins. You can add oilatum etc. Before getting into the bath cover them in emollient (we used diprobase) top to bottom so running your hands down shoulders to hands and not rubbing upwards. Plop them in the bath and no soap. This rehydrates their skin but more than 10 mins you lose the benefit.
Remove from bath and pat with towel - do not rub their skin. Add extra emollient top to bottom again. Leave this to soak in for 20-30 mins. Then...
Use steroid cream and don't be shy with it. We had eumovate. Not hydrocortisone 1% like your GP probably tries to fob you off with. 1cm of steroid cream per area (we did this for each wrist and hand for DD). Use the steroid cream for 2-3 weeks (morning and night if needed). When the skin has healed you must wean off the cream slowly: so one week apply nights only; next week every other night; third week every third day. The reason the eczema returns is we stop the cream too quickly and go cold turkey. If you use the cream like this it should knock the outbreak on the head so you're not constantly using it for months (which is where side effects can occur).
I stopped using fabric softener in my wash too. Generally highly scented products are the culprit.
If there is eczema on the face you need to use protopic on it instead of steroid cream. It's safer.
Do not cut out dairy if your friend's cousin's son's dog tells you they did and it was the answer they are most likely wrong. Kids need dairy for calcium to grow. Plus if someone is allergic to milk it's usually the protein and this protein is in all animal milk.
Ditto the not washing daily. You need to bath them to remove allergens from their skin (dust mites or pollen etc) and rehydrate their skin. Just ditch the actual soap.
Be prepared for pjs to become sodden with creams/emollients - it never seems to wash out. Sorry.
Also when hair washing do it and rinse it out then get them out of the bath. Don't let them
sit in the suds.
Anyway if you follow this routine (yes it's a ball ache) their skin can relearn how to behave. It really does work especially if you start young. DD was eczema free by 8/9.
Also I used sunsense sun cream as that was recommended by the eczema team.
Really hope that helps.