As with Begum, the Home Office stripped the woman - of Bangladeshi heritage but born in Enfield, north London - of her British citizenship.
"We hope you understand our position in this respect and why we must, therefore, assist Shamima in challenging your decision to take away the one thing that is her only hope at rehabilitation, her British citizenship", the family's letter said.
In a Sky television interview, Begum said she had lost two children and would not want anything bad to happen to her third child.
It said Shamima Begum's status would now be a matter for British courts to decide.
"There is no question of her being allowed to enter into Bangladesh", Shahriar Alam, the state minister of foreign affairs, said.
She went on to say she may try for citizenship in the Netherlands, where her husband is from.
But CNN had obtained her birth certificate which shows she was born in Bergen county, in the state of new jersey. Asked whether she could change or be rehabilitated, she said: "I am willing to change".
She denied making propaganda for IS, telling local media "people should have sympathy towards me for everything I've been through", but conceding, "When I saw my first severed head in a bin it didn't faze me at all".
Begum, who gave birth to a son, Jarrah, last Sunday, pleaded to be allowed back to the United Kingdom but sparked outrage by failing to apologise for joining the terror group.
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Begum, 19, is nine months pregnant and living in a Syrian refugee camp.
Firstly, we wish to make clear, that along with the rest of the country, we are shocked and appalled at the vile comments she has made to the media in recent days.
"They haven't given me that courtesy", she said.
"These are not representative of British values, and my family entirely reject the comments she has made".
"We are sickened by the comments she has made, but, as a family man yourself, we hope you will understand that we, as her family can not simply abandon her". Now, she wants to come home.
Jihadi bride Shamima Begum has said the United Kingdom government is "making an example of her" by stripping her of citizenship and forbidding her return.
"We do not comment on individual cases, but any decisions to deprive individuals of their citizenship are based on all available evidence and not taken lightly", a spokesperson said. "I think she should be brought back".
"But when someone turns their back on (our) fundamental values and supports terror they don't have an automatic right to return to the United Kingdom", he said.
The case involved another jihadi bride, identified only as "G3", who fled to Syria to join ISIS with her two children, then aged one and two, in November 2016.