The family had asked that half the remains be returned to them with the other half scattered in the grounds.
Half were returned but the remainder had been wrongly used in an un-witnessed scattering earlier that day at  Weston Crematorium, Worle.
The two workers lost their jobs and Dignity, which runs the crematorium, apologised for the family's distress.
Instead of admitting their mistake, two members of staff, who have been described as "very experienced", tried to cover it up by using another person's ashes for the ceremony in front of the family.
Eventually, they admitted what they had done to their manager, and Dignity - which runs the crematorium on behalf of North Somerset Council - started an "extensive" disciplinary hearing.
In a statement Dignity said it was an "isolated incident" and would look at why "very experienced staff failed to follow our established procedures".
"Following disciplinary hearings, two employees are no longer in our employment. The family and North Somerset Council have been kept fully informed throughout."
A North Somerset Council spokesman said Dignity had kept it "fully informed during the process".
"We are satisfied that they have investigated the matter thoroughly."

The 24-year-old has agreed a two-year-deal and will arrive following his commitments with the Stormers and Western Province in South Africa.
He is the son of former Springbok Guy Kebble and won the 2012 Under-20s World Championship with South Africa.
"I try and bring an edge to the game and make an impact," Kebble told the Pro12 club's website.
"I've watched all of the Glasgow matches in the Champions Cup this season and northern hemisphere rugby is getting very exciting. I'm looking forward to playing in a competitive European league.
"I know Dave Rennie is one of the best coaches in the world, so it's an exciting prospect to work under him next season."
Kebble will join current team-mate Huw Jones in Glasgow, with the Scotland centre signing a two-year contract with the Warriors earlier this month.
"Huw and I live together in Cape Town," he explained. "We didn't really talk about it too much before it happened, but now it's nice to know there will be a familiar face in Glasgow."
Last week, BBC Scotland revealed Kebble's expected arrival, with the new recruit considered a project player by Scottish Rugby, who have monitored him for several years.

West Yorkshire Fire Service said half of Freeston Academy in Normanton, near Wakefield was ablaze at one point, leaving the building badly damaged.
More than 50 firefighters attended after the alarm was raised at 09:10 BST. The blaze was brought under control by about 12:00.
The fire service said there were no injuries and students were unaffected.
Local residents were advised to keep windows closed and stay inside at the height of the fire.
Ian Bitcon, area manager for the fire service, said the blaze was in the roof of the school which was "difficult to deal with due to access".
He said: "We've been very fortunate in that the school's unoccupied and there's been a very good water supply.
"We appear to pretty much have it cracked now."
A caller to Radio Leeds said: "I was on my way home when I saw this massive smoke and flames.
"They turned us all away and stopped us all going up the street.
"There's loads of kids here waiting for their GCSE results and they're all coming away in tears."
Students at the school were later directed to the sports hall to collect their exam results.
A woman whose daughter had been to collect her exam results at the school said: "It's been a crazy day".
She told BBC Radio Leeds: "It's been an emotional rollercoaster. First, getting up and waiting to come in and pick up the results.
"But then to hear the school was on fire. It's just been an utter drama."
In a statement, the school said: "Our main priority was the safety of our staff, students and contractors working on site, and to ensure that our year 11 students were able to collect their GCSE results.
"Following advice from the fire service, all students were able to collect their GCSE results from outside the sports hall.
"All staff on the site were accounted for and no one was hurt in the fire."
The ashes of a stranger were scattered in front of a family by two cemetery workers trying to cover up a mistake.
[NEXT_CONCEPT]
Glasgow Warriors have confirmed the signing of loose-head prop Oliver Kebble for next season.
[NEXT_CONCEPT]
A large fire broke out a school as students gathered to collect their GCSE results.