Courtney Brierley, 21, was jailed for 21 years after the attack at a home in Walkden, Greater Manchester, in December 2017.
Within seconds, flames engulfed the property and the blaze claimed the lives of siblings Demi Pearson, 15, her brother Brandon, 8 and sisters Lacie and Lia, aged 7 and 3.
Brierley was accused of encouraging the attack and was found guilty of four counts of manslaughter, but cleared of three counts of attempted murder.
Zak Bolland, Brierly’s then boyfriend, and David Worrall were each convicted of four counts of murder and jailed for life.
Following a hearing in London on Thursday, the Court of Appeal dismissed Brierly’s appeal against her conviction and a separate appeal against her sentence.
Lord Justice Holroyde said: “There is no arguable ground on which the safety of the convictions can be challenged.”
Manchester Crown Court heard how Bolland had been involved in a feud with Kyle Pearson over £200 damage to the defendant’s car.
The squabble promoted a series of tit-for-tat attacks which culminated in the petrol bomb attack on Michelle Pearson, 36, home.
“There is no arguable ground on which the safety of the convictions can be challenged”
Lord Justice Holroyde
Fuelled by drink and drugs, Bolland and Worrall filled two glass bottles with petrol bought from a local garage and stuffed the tops with tissue paper.
Through an open window, the pair then threw the petrol bombs into Kyle’s mothers home.
One of the bottles was hurled further into the home, blocking the exit to the ground floor and trapping the victims.
Kyle escaped the blaze with his friend Bobby Harris, but his siblings weren’t so lucky.
Mrs Pearson woke up and screamed: “Not the kids! Not my kids!”
In an attempt to save her children, Mrs Pearson dialled 999, but was overcome with heat and smoke before finishing the call.
Heartbreakingly, three children who were sleeping in a front bedroom all died in the blaze.
Kyle’s mother was rescued with her youngest daughter but sadly, Lia died in hospital two days later.