Gary McCourt, 49, was found guilty of killing Audrey Fyfe in Edinburgh when he hit the back wheel of her bike.
Mrs Fyfe, from Joppa, died two days after being struck by McCourt at the junction of Portobello Road and Craigentinny Avenue on August 9, 2011.
McCourt was convicted of causing death by careless driving and sentenced to 300 hours of community service and banned from driving for five years.
After McCourt was found guilty, it emerged that in 1985 he had hit and killed 22-year-old cyclist George Dalgity on Regent Road in Edinburgh, for which he served two years in jail.
On Tuesday, Ms Fyfe’s family will lodge a letter of complaint with the Crown Office, saying McCourt should be banned from driving for life.
Her widower Ian said he did not want McCourt to be sent to prison but a message needed to be sent out to other drivers.
He said: “He’s proved his driving abilities and attitude to other road users is unbelievable and now he’s going to have the option of a third attempt. Who will be the next one to suffer from his disregard for other people?
“He should be removed from driving on public roads – it’s the only answer. While I wouldn’t advocate prison, he should be given some sort of punishment that repays what he’s done.
“What kind of message does that send out to other drivers? I’m just disgusted.”
Mrs Fyfe’s daughter, Linda Hamilton, said the family were shocked with the sentence.
She said: “I think we were numb to start off with, it fairly quickly turned to despair. I just don’t understand it.”
The family are working with cycling charity CTC on the campaign for an appeal.
A spokesman for the Crown Office said the sentence was still being considered. He said: “Crown Counsel will give careful consideration as to whether the sentence was unduly lenient.”
Information is currently being gathered by the Crown Office & Procurator Fiscal Service to feed back to the Crown Counsel who will consider whether to pursue an appeal of the sentencing in this case. To feed into this process, Cycling Scotland has written to the Crown Office & Procurator Fiscal Service highlighting concerns about the sentencing.