Store manager Geraldine Newman, her daughter Shannon, 11, and six-year-old son Shane were found at their terraced house in Allerton Bywater on Tuesday.
A friend found Ms Newman's body on the ground floor of the property after becoming concerned.
She then called police, who discovered the children's bodies upstairs.
Ms Newman's estranged husband Paul Newman was found dead on cliffs in South Stack, Anglesey, North Wales, hours later.
Detective Chief Inspector Warren Stevenson said: "While our investigation into the full circumstances surrounding the deaths is ongoing, we can say that this appears to have been a domestic-related incident and we are not looking for anyone else in connection with it."
Tributes were paid to the children, with Shannon described as "a bright, intelligent, enthusiastic, hardworking and caring student" and Shane as a "a caring, lovable young boy".
Their mother worked at Wilko for 23 years and was described by a spokesman for the retailer as a "loyal and enormously respected member of the team".
He added: "This is tragic news and has devastated everyone who worked with Geraldine as well as impacting team members across the company.
"Our heartfelt thoughts and condolences are with her family, friends and colleagues at this very difficult time and everything is being done to support those team members who are affected by this tragic news."
On her LinkedIn page, Ms Newman, 51, described her children as "the light of my world".
Neighbours were in tears when they heard the news of their deaths.
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