This page is the best description I have read so far of the ailment itself:
http://www.radix.net/~hogue/mhe.htm
It sounds like a horrible thing, basically generally benign tumors causing bones to grow abnormally. I did a few searches on it, and came up with nothing in terms of clinics claiming to treat this disorder. It plagues mainly children, full grown adults should be close to the end stage of the ailment. A few other things I read suggested that this ailment is caused by malformation of stem cells during the development of the embryo. Since it is a bone disorder, marrow is obviously involved. I have read of a clinical trial in British Colombia, Canada where they are testing blood from family members that have the disorder, but again, no trials involving stem cells to help with a possible cure.
I noticed that you are in Oregon. If this family is also there, have they sought out the best possible medical care? If these were my children, I would take them for a week to MD Anderson Cancer Center in Houston, Texas for a full workup. They are the best in the country, possibly the best in the world. I understand fully that this ailment is not a cancer, and usually not a malignancy, but if marrow transplants could help, then they could be done legally in the USA at a place like MD Anderson. St. Jude is another talked about hospital (founded by Danny Thomas) but I know nothing about it other than the TV commercials. They do say "no child turned away due to inability to pay" if money is an issue. MD Anderson also has full financial aid available.
Again, perhaps these children have good doctors, but do they have the best available ones? Even if they do, a second or third opinion could be beneficial.
Marrow has been used in cancer treatments for several decades, so these people may not need to pay huge money and leave the country to have treatment for this issue done.
The difference between a "stem cell treatment" and a "bone marrow transplant" is very subtle. With a bone marrow transplant, you are actually getting stem cells, it is just called a marrow transplant. Even a blood transfusion gives you some stem cells for that matter.
Even if they wanted to, it does not appear that anyone has done any stem cell treatments for it at this time outside of the USA.