Rizlaine Boular, 22, has been jailed for a minimum of 16 years, and her mother, Mina Dich was jailed for six years and nine months.
Dich will spend a further five years on licence.
A third member, Safaa Boular, 18, is to be sentenced at a later date.
A fourth person, Khawla Barghouthi, who was a friend of Rizlaine, faces jail for not alerting authorities to the plot.
Boular planned to stab random members of the public around the Palace of Westminster to cause widespread panic, injury and death, the Old Bailey heard.
She had taken the idea from her younger sister Safaa, who was in custody over an attempt to become a jihadi bride in Syria.
The sisters spoke of an Alice in Wonderland themed tea party in coded phone calls, with the elder sister cast as the Mad Hatter.
Boular, 22, pleaded guilty to preparing acts of terrorism.
Her mother, Dich, 44, admitted helping her, and was jailed for nearly seven years.
Judge Mark Dennis said Dich “failed in her parental role” to step in and stop the attack, and said she played a “significant role” in the radicalisation of both of her daughters.
He told the elder Boular she planned a “wicked act”.
He added: “There are individuals walking the streets today whose lives could have been irreparably damaged or lost had it not been for the intervention of the police and security services.”
The pair did not react as they were sentenced.
The court heard that Rizlaine and Safaa discussed the plot with Dich, before Rizlaine and Dich went shopping for knives and a rucksack.
Rizlaine practised the attack in a bugged conversation at friend Barghouthi’s home, as the pair laughed about whether she might “flop so badly” and cut her arm by accident.
When Rizlaine was arrested, she shouted “f*** you* at police.
She was shot in the stomach three times by an officer who thought she had something in her hand.
In mitigation, her lawyer Imran Khan said: “In short, Rizlaine Boular embarked on this course of conduct because she wanted to die.
“She knew as soon as she produced a knife in the vicinity of the Palace of Westminster police officers would swoop and kill her and that’s what she wanted at that time.”
Mr Khan added that she had been radicalised online after being sacked from a job in marketing because she wore Muslim clothes, and she had suffered an abusive marriage to a local imam.
But he said she had put her past views behind her.
Being shot on arrest was a “constant reminder” he said, of what had happened, and “the fact she realised when she was shot she did not want to die”.
In mitigation for her mother, Dich, Keiran Vaughan said she played a “lesser role” in the plan.
Barghouthi’s lawyer said the 21-year-old did not realise how serious the defendant had been to carry out the attack, and said she had been shocked to listen again to the recordings of their conversations.
She will be sentenced next Friday, and Safaa Boular will be sentenced at a later date.