"My client is innocent and of course she wants her case tried," Schürrer's lawyer Per-Ingvar Ekblad told the Expressen daily.
Since the verdict, Schürrer and her legal counsel have been putting together a 17-page application for leave to appeal, which they finally submitted to the Supreme Court (Högsta Domstolen, HD) on Tuesday.
After the initial guilty verdict by the Västmanland District Court in 2008, Schürrer and Ekblad took the case to the Court of Appeals, only to be told the verdict would stand.
At the time, Ekblad argued that there were no clear legal grounds for the conviction, and said he would seek leave to appeal to the Supreme Court.
He said the evidence presented did not meet legal requirements for a conviction and added that there was scope to argue his client had not been found guilty "beyond reasonable doubt".
With the thorough new application, Ekblad believes there is a strong chance the case will be heard by the Supreme Court.
"Otherwise we wouldn't have done it," he told Expressen.
"Now we're hoping for an acquittal."
Christine Schürrer had been in a relationship with mother Emma Jangestig's then boyfriend, Torgny Hellgren. According to prosecutors, her obsession with her ex-boyfriend served as the motive for the killings of the two children.
Investigators were never able to tie Schürrer to the crime scene with physical evidence. Instead, prosecutors based their case on strong circumstantial evidence.
Despite the lack of fingerprints or DNA evidence, the court ruled that there was "overall convincing evidence" against Schürrer.
A network of people have sought to help Schürrer in her case since the verdict, but Ekblad told Expressen that only he and his client had compiled the new application.