A two-day inquest heard that the children, from Milkwall, Gloucestershire, were found dead at Pontesbury Hill, Shropshire, on July 16 last year.
All three had suffered a severe neck wound inflicted with the Bowie-type knife, while the two girls had been repeatedly stabbed in the chest.
The inquest heard that Mr Fuller, a paper mill worker who had a degree in molecular biology, drove the children away from his marital home on the morning of July 12 after agreeing to split up with his wife.
During the inquest, Mr Barkley heard that Mr Fuller's wife, Ruth, had been suffering from mental problems and attempted to stab herself and take an overdose after the children left.
More top news
X-Factor winner Sam Bailey is gearing up for a 100-mile charity bike ride.
East Midlands weather: Starting dry, with clouds thickening
West Midlands weather: Staying dry overnight with some patchy amounts of cloud and clear spells developing