Baxter grabbed four-year-old Laianah on Boxing Day 2019 and put her in his car so quickly she bumped her head, leaving a "very distressed" Ms Clarke and their other two children behind screaming and crying, a witness said on Friday.
The witness, who didn't know the family, was so upset by what she saw she felt compelled to report it to police.
Baxter took his daughter to NSW for more than two days before Laianah was returned to Ms Clarke following police intervention.
However, Detective Sergeant Derek Harris - from Morningside Child Protection Investigation Unit - said what Baxter had done "wasn't a crime".
Barely two months later, Baxter killed Ms Clarke and their three children, setting them on fire in a vehicle in suburban Brisbane.
"There's no family law court order, there was no child protection orders in place to stop Rowan legally having access to that child (on Boxing Day)," Det Sgt Harris told the inquest on Friday.
"What he did was disgusting and inappropriate ... it was his only way to cause harm to (Hannah).
"But unfortunately it was not something that an investigator could progress - it wasn't a crime."
Det Sgt Harris said it wasn't until he reviewed the matter after the daughter had been returned that a police protection notice and a domestic violence order were in place.
He said he considered it a custody dispute and referred the matter to the Department of Child Safety.
"I don't condone it (Baxter's behaviour). It was done to ... cause emotional distress," he said.
"(But) my role as a detective is to investigate crimes against children ... unfortunately it is very black and white."
The deaths of Ms Clarke, her three children and Baxter are the subject of the inquest that started in Brisbane on Monday.
Ms Clarke was leaving her parent's home in Camp Hill to take her children - Aaliyah, six, Laianah and three-year-old Trey - to school on February 19, 2020.
Baxter got into the car, poured fuel inside and set it alight.
The badly burnt adults escaped the vehicle, but Baxter, 42, stabbed himself with a knife, dying nearby.
Ms Clarke died later the same day in hospital.
After they separated in late 2019, Ms Clarke feared for her life and was also worried Baxter would take the children.
Baxter continued to see his kids, but on Boxing Day took Laianah after the family met in Bulimba.
Julie Ann Humphries did not know Ms Clarke or her family, but was so concerned after witnessing the incident she approached a police officer nearby.
"I saw a woman with two children who were very distressed. The children were crying and screaming out 'no stop'," she told the inquest.
Dr Humphries said Baxter wouldn't have had time to secure his daughter with a seatbelt before leaving "in a hurry".
"Unfortunately she bumped her head on the way into the car," she said.
"A loving father who cared for his child wouldn't behave that way."
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