A home induced-miscarriage is NOT safe. Please do not go this route. Even if one of these methods causes a miscarriage, it could be imcomplete and lead to severe problems and possible infertility if ANY of the fetal tissue is not expelled from the body.
I do know the method that you are referencing, but it is not just Vitamin C that needs to be used, it is a number of things together which can be dangerous. It also is NOT effective after being 3 weeks late on your period (7 weeks pregnant). Why does your sister not go to Planned Parenthood? An abortion there would likely be free and your parents would not need to know. She could have a surgical (D&C) abortion which they could put her under sedation and she would have virtually no pain. The method that you are inquiring about is VERY similar to the medical abortion and is VERY painful. She will have 3 to 5 days of severe cramping and bleeding (potentially longer on bleeding) and will likely see the fetal tissue (clump = baby) expelled. It will not be pleasant.