PHILADELPHIA — A brother and sister convicted of cyberstalking linked to the killing of the brother’s ex-wife had their freedom of speech rights violated, and their trial was tainted by irrelevant evidence, their lawyers argued Wednesday.

David Matusiewicz and Amy Gonzalez were sentenced to life in prison after their father fatally shot Matusiewicz’s ex-wife and her friend at a Delaware courthouse in 2013. The killing of Christine Belford capped a three-year campaign of torment and stalking waged by the family against the woman in an effort to regain custody of the three children she had with Matusiewicz, according to prosecutors.

Attorneys for Gonzalez and Matusiewicz told a panel of appeals judges in Philadelphia that at least some of what was used as evidence was protected speech under the First Amendment and that jurors shouldn’t have heard certain details contained in a family court order terminating Matusiewicz’s parental duties.

Prosecutors said the family accused Belford in a series of online postings, emails and letters of sexually abusing one of the former couple’s daughters. The allegation of abuse has never been proven, and the daughter denied it in sworn testimony.

Matusiewicz had his parental rights stripped in 2011 after he and his mother kidnapped the children and fled to Central America, where they lived for a year-and-a-half before being tracked down. His attorney on Wednesday told the panel of judges that her client’s trial was “tainted” because jurors shouldn’t have heard details about his personality that were contained in the family court order.

During the cyberstalking investigation, authorities found that the family also drafted a “hit list” that included the names of judges and attorneys who were involved in the family court disputes between the former spouses. Prosecutors said life imprisonment for the family was absolutely warranted, as it was the only way to keep the former couple’s children safe.

The defendants’ mother, Lenore Matusiewicz, died in prison at age 71. Their father, Thomas Matusiewicz, killed himself after shooting Belfort and her friend as they arrived at a courthouse for a child support hearing.