Is it permissible to move the mother's body to be buried with her two daughters and her husband in a private cemetery, and would that be a violation of her will or cause her distress?

It is not permissible to exhume the mother's grave and move her; that is forbidden. The grave is a confinement for the deceased and should not be exhumed as long as the deceased is within it. The jurists have agreed on prohibiting the exhumation of a grave except for a valid excuse, such as the land or shroud being usurped, or money falling into the grave. What you mentioned about the desire to be buried near her is not an excuse that permits the exhumation of the grave.