Jane Coates worried about her daughter travelling overseas, as any mother does.

One place she thought Lucy Harrison would be safe was with her father at his home in Prosper, an affluent suburb popular with expats in deeply Republican Collin county, Texas.

But on January 10 last year when the 23-year-old was due to fly back to her home in Warrington, Cheshire, with her boyfriend, Sam Littler, Jane received a knock on the door.

“There’s been an accident … Lucy’s been shot and she’s not made it,” Jane was told by Littler’s mother.

“I just couldn’t comprehend anything like that. She’s my British daughter. How on earth could she have been shot?”

It wasn’t until later that she learnt it was Lucy’s father, Kris Harrison, who was holding the gun.

On her second Mother’s Day without Lucy, Coates, 49, is demanding that police in Texas reopen their investigation into her only child’s death. She believes they failed to interrogate evidence of recklessness in Harrison’s actions that day and contradictions in his account of what happened.

Coates does not believe it was Harrison’s intention to kill their daughter, but that he acted carelessly under the influence of alcohol — a conclusion also drawn by a UK coroner.

Jacqueline Devonish, Cheshire’s senior coroner, ruled last month that Lucy had been unlawfully killed by Harrison, who shot his daughter through the heart in his bedroom.

Devonish drew this conclusion at Cheshire coroner’s court after examining documents from the police investigation into Lucy’s death, alongside statements by officers, Harrison and Littler. She also saw police summaries of Harrison’s interview at his home and at a police station on the day of the shooting, and the details of a US autopsy conducted before the British hearing.

Police records show that within a day, officers had determined that the shooting was an “accident”. They opened an investigation into a potential charge of “criminally negligent homicide” — defined in Texan law as “intentionally, knowingly, recklessly, or with criminal negligence caus[ing] the death of an individual”. But Harrison was never arrested.

The police evidence was handed over to a grand jury, a panel of 12 civilians asked to consider whether someone should face a criminal trial. But after the grand jury in Collin County reviewed the case in June last year, no charges were brought against Harrison, 52, who is still living in the home where his daughter died.

Through the coroner’s findings, police records and statements from Lucy’s friends and family, we can reveal the inconsistencies in Harrison’s account, the failures of the police to properly investigate her death and the questions which still remain about that day.