I make my own soap (body soap) that I then used to make my own laundry soap. We have hard water and it was not effective for us. The clothes did not get clean and after a few washes, they were not smelling fresh. It didn't make a difference with dd's eczema, either, so not worth it.
My dd has severe eczema, as well. It becomes more severe if its allowed to get out of control. Making my own body soap (just lye, lard and water) has shown the biggest positive change in her eczema. By far, the #1 culprit with her skin issues, though, is her diet. We eat no or almost no processed food (I cook 95 - 99% from scratch, the only things I don't make are bread, crackers, and potato chips, but these are all-natural organic). If something is processed, it's minimally processed and I make sure all of the ingredients are whole foods and no chemicals. She doesn't eat fast food at all and never has. None of us do. Dd is in charge of her diet now (she's 10) and she knows what causes issues and what doesn't. She gets to choose if she wants the special treats. For example, in Feb. she had 3 school birthdays (including her own) and 3 family birthdays (including hers and dh's). She chose whether or not to eat the store-bought cupcakes, etc. She chose to indulge every time and now she is suffering for it. Her legs look horrible and her sleep is disturbed from scratching all night. I hate to use it, but right now the only relief is hydrocortizone cream.
So, for us, laundry soap did not make a difference and we are able to control her eczema in other ways without bothering to make our own laundry soap. Diet and body soap have been the keys for my dd. HTH!