I do not believe that home schooled children who are taught by their family members are any less successful than other students. Many home schooled children actually graduate ahead of time or work at a faster or more advanced pace. I believe that home schooled children can be just as successful as children who go to traditional schools.
Homeschool kids are very successful because they get one-on-one attention, even if that attention is from parents. Family members are perhaps the best people to teach kids since parents and relatives are the best teachers in general. Learning from relatives should be easier since kids already know their teachers and feel more comfortable with them.
No, children who are home schooled by family members are not less successful, because the children have the emotional support of their families. The children are less likely to have emotional problems, and they are less likely to fall to peer pressure. The home schooled children have the receipe for success.
Perhaps it could be safe to say that maybe children who are home schooled by family members are more successful because they are able to concentrate more accurately because they would feel more comfortable at home as opposed to a school which could make some children nervous and interfere with their studies.