Removing Mold From Fabric

the only solution i have ever found to remove mould staining in 30 years of commercial laundry and drycleaning is chlorine belach. Hydrogen peroxide may work as well especially with coloured items but this is entirely dependant on how "fast" the stain is.
There are 3 things that affect the way chlorine bleach works. Strength of solution time and temperature.

Others claim exposing the soaking solution to sunlight will increase action I have my doubts.
I cant give you a reccomendation on how much bleach to use. go with the manufactureres reccomendation then try doubling it and increasing the temperature and time.

At some point the material may be degraded by the bleach so be prepared for it to fall apart or have a less usefull lifespan.

You say you CAN remove it and put it in the washer, but then say the mold won't come out.

Have you already washed it? If so, did you also dry it in the dryer? Cause that can set a stain.

I have successfully used Krud Kutter (paint removal section of Home Depot - although it is not a toxic paint remover. I don't know why that is where they place it.) It should be with the Goo Gone. Safe for most surfaces I've used it on so far, including leather, although you will want to test in a non conspicuous place first. I use it in place of bleach in the washer since it is non - toxic and doesn't eat the cloth like bleach. Removes grass, red clay, blood, red kool-aid, mold, rust, etc.

Try it full strength rather than the diluted version.