Giordano, who has stage 4 breast cancer, made national headlines when she lost custody of her two children. A Durham judge ordered they should live with their father in the Chicago area.
Giordano's attorney filed the notice of appeal shortly before noon Tuesday - the day before the deadline. It's unclear if it will delay the court order that the kids move to the Chicago area by mid-June.
"Today, my attorneys have filed an appeal on my behalf and are exhausting every avenue to help me keep my children here at their home in Durham," said Giordano in a statement to the media. "It is absolutely outrageous - and unprecedented - that a court would cite my illness as the reason to take my children from me, and uproot them from their home. I am confident that we will prevail."
While Giordano's case has won her national sympathy, court documents show neither of the children's parents have been angels. They got into an altercation and both spent the night in jail.
But, Giordano has more strikes against her. Her ex-husband was able to land a job in Chicago and find a house in a good school district, while Girodano is unemployed and facing ongoing cancer treatment.
She also confessed to having an adulterous relationship, and spending days out of state with a married man while her children were with their grandparents.
On another occasion, court documents show Giordano did not make suitable arrangements for her children on a day a doctor told her she was going to be admitted to the hospital.
The documents say she took her children with her to Duke Hospital.
To avoid calling child protective services, a doctor took the children home with her. The doctor called it a crisis, and Giordano called it a great opportunity for the children to get to know the person treating their mother.
Finally, when the children were visiting their father, Giordano failed to send her son's epinephrine pen. The wrote that shows she has difficulty separating her anger from the well-being of her children.
However, the judge did state she could get 50 percent custody if she moves to Chicago.
That's something Giordano is unwilling to do.
"It really would be dangerous for me to move away from my support system and my medical team," Giordano said in a previous interview..
Currently, a United Airline's flight attendant is offering buddy passes so Giordano can fly to see her children.
She's also seen hundreds of dollars pledged to help with medical and legal bills.