Samia Shahid, 28, from Bradford, died last month in northern Punjab.
Her former husband Chaudhry Muhammad Shakeel, who is accused of murder, has confessed to strangling her with a scarf, local police have told the BBC.
He and her father Chaudhry Muhammad Shahid were remanded for a further five days by a Pakistani judge.
Mr Shahid is being held as an accessory to murder.
Both men were remanded for four days at their first court appearance on Saturday.
Police in Pakistan have told the BBC that Mr Shakeel, who is also Ms Shahid's cousin, has confessed to her murder.
Ms Shahid had been visiting relatives in the village of Pandori when she died and her relatives had initially claimed she died of a heart attack.
Her second husband, Syed Mukhtar Kazim, believes she was the victim of a so-called honour killing as her family did not approve of their marriage.
A post-mortem examination has since confirmed she died as a result of being strangled, police say.
Like last time Ms Shahid's father and former husband had their faces covered as they went into the court although the media were allowed inside the courtroom this time.
In court they uncovered their faces and both men appeared calm and did not speak as the judge remanded them in custody for another five days - a period of time requested by the investigating officer.
Police told me on Monday that Chaudhry Muhammad Shakeel had confessed to Samia's murder.
However, her second husband said that held little legal weight and that he was more concerned with what Mr Shakeel would say in court.
The ex-husband and father of a beautician allegedly murdered in a so-called honour killing in Pakistan have appeared in court for a second time.