Maria De Jesus, 32, from Dagenham, Essex, was discharged from Queen's Hospital, Romford eight days after the bungled operation but she was forced to re-admit herself to hospital six days later with crippling stomach pains.
She miscarried two days later - the same day medics finally read a report confirming the mistake.
Her appendix was not removed until 19 days after the wrong procedure, when the mother-of-two died on the operating table.
Her family has now vowed to take legal action against Barking, Havering and Redbridge Hospital Trust.
An inquest heard teaching assistant Mrs De Jesus developed severe sepsis as a result of the appendicitis and died from multiple organ failure.
Coroner Chinyere Inyama said 'a lost window of opportunity' could have saved Mrs De Jesus.
Husband Adelino De Jesus, 53, said: "The procedure to remove the appendix when Maria was pregnant was not simple. We were told at the inquest that the surgeons had to 'feel' for the organ.
"But they removed the wrong one. We feel that this was negligent.
"My wife's death could have been prevented, I am sure of it.
"By the time they realised how serious the situation was - and they promised us all the best consultants, it was too late.
"This is neglect, this is an unlawful killing. If my wife had been given treatment by fully qualified staff and people were informed of the mistake earlier she could still be alive."
The hospital trust has admitted liability for her death at Queen's Hospital in Romford in Essex in November 2011 and has apologised to her family.
The General Medical Council is currently investigating eight medical staff, including a senior surgical consultant Dr Babatunde Coker over the death.
Mrs De Jesus would have been 34 this month. She had three older children. Her daughter Catarina, 10, said: "We have put the balloons up because it was mum's birthday and it's good to celebrate it."
Her son Pedro, 16, added: "It feels like such a big injustice."
Averil Dongworth, chief executive of the Barking, Havering and Redbridge Hospital Trust, said in a statement: "The staff involved in Mrs De Jesus' care have been deeply affected by her death.
"An extensive trust-wide action plan was drawn up following Mrs De Jesus' death in 2011 to ensure that such a tragic incident will not happen again."
The coroner recorded a narrative verdict.