You would have to get it entirely off the roots somehow because even one small white spec would just overtake the soil if it was brought in. Mycelium does extremely well in transplants. If you washed of the roots thoroughly you might get rid of it. I don't know if spraying with peroxide would hurt it at all. I use it with positive effects. If you do transplant it try to keep the temperature as low as you can with stressing the plant for a week or week and a half. And when the mushrooms come up try to pick them before their veil tears and they open releasing spores, because spores will stick on you and will get everywhere and maybe into other plants.

If it wasn't you mother plant I wouldn't worry about but since she's gonna be around for awhile something needs to be done. Even if the transplant doesn't get rid of it your roots will be better off in less of it.When you dig around in the soil do you notice white thread like almost mold looking growth?