Foster, who resigned from Surrey Police in 2009 after being arrested for drink-driving, had a short fuse and had lost his temper over trivial matters many times before, Lewes Crown Court heard.
In 2010 Miss Cooper, who was a detective constable in Surrey Police's domestic violence investigation unit, told friends that her relationship with Foster had become strained and he would smash up items around the house in a rage.
She considered leaving him but was persuaded to stay, and they discussed how he could get help for his anger management problems.
Miss Cooper gave birth to their second child in August last year and was still on maternity leave when she was murdered.
The day of the killing began with the family attending the christening of a friend's grandson, at which Foster was made a godfather.
However, the couple got in a row about losing their baby changing bag, which contained a camera and nappies. They sat with their backs to each other in the church and left early without attending the reception.
They continued arguing through the afternoon. Foster stormed out of their house in Haslemere, Surrey, and went to a local Waitrose to buy two bottles of wine, some of which he drank on his way home.
The martial arts-trained former policeman claimed that on his return Miss Cooper came at him with a knife while he was holding Isabelle, and said he hit her once in self-defence with the baseball bat, which he kept for self-protection.
However, a post-mortem examination showed that his partner was hit more than 10 times with the bat and stabbed through the throat with a knife while she lay unconscious.
Benjamin Aina QC, prosecuting, said: "On many occasions Mr Foster had lost his temper on trivial matters and gone over the top.
"The violent attack is another indication of another over-reaction on his part, this time with tragic consequences."
Foster cleaned up the blood-soaked crime scene and took Miss Cooper's body to a nearby beauty spot at Blackdown Woods, near Lurgashall, West Sussex, where he covered her with bracken.
He then took his children one at a time to the home of his grandmother, Marguerite Halkins, 77, and told her that something terrible had happened.
When asked where his mother was, three-year-old Joshua, who was unusually quiet and subdued that day, replied: "Sleeping."
The former detective also sent a number of text messages that afternoon in an attempt to create an alibi for himself, concocting a story that she had left him after discovering he was having an affair.
He wrote to a colleague: "Hi mate, Heather walked out on me. Explain later. Left me with the kids. Please can you cover tomorrow?"
Relatives became concerned and called police, who found Foster at Ms Halkins' house. He told the officers: "You should arrest me." When they asked him what for, he replied: "Murder."
Foster was jailed for life with a minimum term of 17 years yesterday (Tue) after pleading guilty to murdering Miss Cooper on October 16 last year.
Judge Richard Brown said he was an "extremely dangerous individual" who may never be safe for release.
He said: "This was a wicked, savage and senseless attack on a young mother in her own home.
"Not only have you taken her life, you have also deprived Joshua and Isabelle of a loving mother and, no doubt, devastated her family and friends."
Philippa McAtasney QC, defending, said Foster's life spiralled downwards after his father Nick was murdered in an armed robbery in Sierra Leone in West Africa in 2009.
This led to him drinking and he was caught driving over the limit, putting an end to his police career. In May 2010 he was sentenced to six months' imprisonment, suspended for a year, for dangerous driving and drink-driving.
Miss Cooper, who grew up in York, joined Surrey Police in 2003 and worked in the Public Protection Investigation Unit based at Guildford police station.
Craig Denholm, Surrey Police's Deputy Chief Constable, described her as "a super-mum, a super-person and, indeed, a super-cop".
