Geraldine Newman, 51, daughter Shannon, 11 and son Shane, six, were found on Tuesday in Allerton Bywater.
The children's father, Paul Newman, 42, from Normanton, was found dead on cliffs on Anglesey the same day.
Mr Newman was charged with common assault on Mrs Newman in July 2013. He received a custodial sentence, West Yorkshire Police said.
The assault case was assessed as high risk, subject to detailed review and monitored for 12 months.
During that time there were no further incidents reported to it, the force said.
There is also to be a full review of the current case, West Yorkshire Police said.
Mrs Newman was found in the house near Leeds and had died of head injuries, a post-mortem examination  showed. Her two children were stabbed to death.
Police said the case was "shocking". They are not looking for anyone else over the deaths.
Mrs Newman, a branch manager for Wilko in Castleford, was found downstairs while the two children were discovered upstairs.
Stacey Swinson, a daughter of Geraldine Newman, said: "What has happened to my family is absolutely tragic.
"I would like to thank everyone for their kind wishes and condolences.
"This is a very difficult time for us and I would ask that people respect our privacy while we continue to grieve with family and friends."
Mr Newman was discovered on a cliff ledge at South Stack, a rocky island about 180 miles away.
A man suspected of killing his family in West Yorkshire had been previously jailed for domestic violence.