A Detergent Free Update

So it has been about 3 weeks since I've rid our house of any products and cleaners that may have detergents in them and been using soap products to clean our house and ourselves.
Here is a couple pictures of her areas that are the worst just before we started using soaps, behind her knee and by her armpit:

I did the soap test on Alivia when I first got the new soap but did not see any improvement, I also feel like there may have been cross contamination with detergents during the 'test' as I had not yet wiped or cleaned down the bathroom. Even though there was no improvement on her skin from the test I am still convinced this is the issue as Hudson too has developed some patches of eczema on his upper arms that are very red and dry- he hasn't started to itch them yet. So even though we're not using detergent products I have not been able to thoroughly get the detergent build up out of our house yet- what is in clothes, carpets, couches, then I think about the car and car seats... OVERWHELMING!
I did start out by washing ALL the kids clothes and bed sheets, doing 2 or 3 HOT rinses, then a normal wash with my new home made laundry soap that has NO detergents then another couple hot rinses. It's impossible to tell though when the detergents are actually out of the clothing or material it may be months before we see a change for the better.
That being said, now that is had become very hot and sunny Alivia has developed white blotchy patches on her arms, where her skin is exposed to the sun (which if I remember correctly she seems to get every summer). Even if I apply sunscreen she has dark tanned spots with blotches of scaly white skin, I think it is more the appearance that is bothersome but it is a never ending battle. So of course I hop on the internet and try and figure out what could be causing this, there are MANY different possibilities and reasons this could be happening- it could just be her eczema as that dry scaly skin won't tan like the rest, it could also possibly be a fungus or yeast on her skin, which could also be why her eczema hasn't cleared up even with a diet change and getting rid of detergents. If there is still a fungus on the skin the eczema can't clear up until that is resolved. SO, another thing to try and solve with hopefully a simple solution of an apple cider vinegar bath! Apple cider vinegar has natural anti- fungal properties so if we eliminate the fungas (which sounds so gross, but no it isn't contagious) then maybe the eczema can finally clear up. I did come across a common skin condition called Pityriasis Alba, which is exactly what her skin looks like (except she's not as dark) and since researching this a couple days ago it seem like Hudson's skin is doing the same thing too. There is no 'cure' and it isn't serious but just one more thing to add to the never ending list of things to figure out.
Both Alivia and Hudson had a very bad breakout of eczema over the past few days, it was almost the worst I have ever seen either of their skin. Alivia's limbs were completely red with a raised rash, she was itching like mad and even getting spots on her neck and face. Hudson's has 'spread' covering more of his arms, some spots on his leg and back of his neck. There are just a couple things that we haven't switched to detergent free (I have ordered them but waiting on them to arrive) it is our sunscreen and toothpaste. We got our sunscreen now and after using it for one day both of their skin has calmed down a little. Crossing fingers this is starting to work.
I also did a third soap test on Alivia this morning and the first one on Hudson. After just a couple hours their skin that I washed with soap and covered with vaseline is barely red and looks much improved. It is also much easier to control it when they are covered in their jammies or long sleeves and pants (which is probably why is seems so much better in the winter). Since their skin seems to get much worse when out in the sun I also ordered some full body swim suits for them from UV Skinz, super pricey but if it helps I can't really put a price on that. In an effort to do whatever I can I also came across these hazelwood necklaces which are said to help eczema sufferers, some says it's hokey pokey but for me it's worth a try.
So that is my update, it really feels like there has been little to no progress over the last few months, I know there has but sometimes I feel like all this work and effort isn't even worth it if it's not solving the problem- helping yes, but I want her to be free of eczema and not have to deal with it into adolescents and adulthood and especially now that Hudson is reacting to something I have twice the reason to solve this problem. So mostly feeling discouraged and depressed lately with a few glimmers of hope but will push through, there has to be a solution out there and one that doesn't involve medications, steroids or the endless use of moisturizers.
Thanks again for reading my ramblings!