Fifty-two-year-old Geraldine Newman's body was found at her home in Allerton Bywater on February 2, 2016, along with her two children, 11-year-old Shannon and six-year-old Shane.
The body of their father, Paul Newman, 42, was found dead at the foot of cliffs in Anglesey , Wales, hours later.
The inquest into their deaths continued at Wakefield Coroner's Court this morning, where it was heard that DNA linked Mr Newman to the killing of his children and his wife before he travelled to Wales and leapt to his death from a 240-ft cliff.
Giving evidence, DS Richard Smith, of the West Yorkshire Police Major Inquiry Team, told the court that Geraldine and Paul had endured marital problems for years, and that Paul had even served time in jail in 2013 for assaulting her.
They had been reunited after his release but they continued to have issues.
Paul suffered from mental health issues, including OCD (obsessive compulsive disorder) and a bad back for which he took strong medication.
He blamed the medication for the changes in his mood.
Toxicology reports after their deaths found that both Geraldine and Paul had traces of anti-depressants in their system, which they had both been prescribed.
Along with the text message Geraldine sent to a member of Paul's family, DS Smith said they found a list of incidents listed below in date order on her work computer involving Paul.
She had also told the headteachers of her children's schools that she was breaking up with Paul.
It was not until February 2, when a friend of Geraldine became worried that the emergency services went to the family home on Beeston Way and made the gruesome discovery.
DS SMith said: "There is no evidence to suggest anybody else had been involved.
"Paul had murdered his wife and two children and travelled to South Stack (in Anglesey) and committed suicide.
"He did so because of the problems in his relationship."
Senior coroner at Wakefield Coroner's Court, Kevin McLoughlin concluded that despite a lengthy investigation, there was still no warning signs of the extreme violence that would occur at the home, and that Mr Newman had not expressed or thoughts about wanting to harm his family.
He recorded a verdict of unlawful killing for Geraldine, Shannon and Shane and a verdict of suicide for Paul's death.