"It's a nightmare," she told AFP, saying she and Christine, 42, are braced to leave friends, family and her job in Rome "because it's the only escape route".
Civil unions became legal in Italy in 2016, but the law on parental rights for same-sex couples is unclear.
Encouraged by several court rulings, local mayors have in recent years been registering both biological and non-biological parents on birth certificates.
But in January, Meloni's interior minister ordered town halls to stop transcribing certificates of children born abroad through surrogacy, citing a recent court ruling.
In response, prosecutors across Italy began contesting birth certificates of children born to same-sex parents -- whether through surrogacy or not.
Chiara is registered as Arturo's mother but is not his biological parent -- meaning his birth certificate, and her rights, could be contested at any time.
So could her rights regarding his baby brother, due to be born early next year.
"The idea that this baby would be put up for adoption if Christine died, instead of being given to me, is absolute madness," she said.
"It would be an absurd brutality."
She asked AFP not to print her surname for fear someone would read about her case, and contest Arturo's birth certificate.
- 'Christian mother' -
Italy's highest court has called on successive parliaments to clarify the parental rights of gay couples -- so far in vain.
Same-sex couples or single women cannot access medically assisted reproduction in Italy and there is no law governing the registration of children conceived abroad by mothers in same-sex relationships, who then give birth in Italy.
In 2016, Italy's highest court supported the transcription of a foreign birth certificate which named two mothers.
And local courts ruled in 2018 that lesbian women who assume parental responsibility for the child their partner carries should have the same rights as heterosexual men whose partners use donor sperm.
Mayors from Milan to Turin, Rome, Naples, Florence, Bologna and Bari have appealed to parliament to legislate as soon as possible.
But following years of inaction among governments of different stripes in the largely Catholic country, campaigners have little hope of change under Meloni.
A self-declared "Christian mother", the leader of the far-right Brothers of Italy party rails against "gender ideology" and the "LGBT lobby" and says children should only be raised by heterosexual parents.
Musician Christine says Meloni has "clearly and explicitly" set out to make same-sex families feel "lesser".
- 'Like an aunt' -
In cases earlier this year, judges in Milan and Bergamo ruled birth certificates of children born to same-sex parents must be altered.
A prosecutor in Padua, northeast Italy, has even instructed the city to retroactively remove non-biological mothers from birth certificates dating back to 2017.
Judges there are currently deliberating whether to amend the certificates of 37 children, the oldest of which is six.
Among those targeted are project manager Alice Bruni and her Irish partner Brona Kelly, mothers to a seven-month-old boy.
Removing Kelly from his birth certificate would make her "like an aunt, a friend -- when we wanted our son together," Bruni told AFP.
"She was in the delivery room with me, she cut the umbilical cord."
The 40-year-old railed against how the case was being heard, with the couple given just 15 minutes in court and no chance to plead their case.
And she said the official letter informing them the certificate would be changed was riddled with errors, including referring to their son as a girl.
Aside from the possibility of losing access to their children if their partner dies or the relationship breaks down, the non-biological mothers risk day-to-day stresses such as not being able to take their child to a doctor without the other parent's permission.
Lawyer Michele Giarratano, who represents 15 of the children in the Padua case, notes those stripped of one parent also "lose the entire family branch of that parent", as well as inheritance rights.
- 'Category B' child -
The Padua judges are set to rule in January and could send the case to Italy's constitutional court, where a ruling would have nationwide implications.
Until then, Padua mayor Sergio Giordani, who has been registering same-sex mothers since 2017, said he will keep doing it.
"I believed I was doing the right thing... and I still do", he told AFP.
"How can I say that this is a category A child, and this a category B one? This one has rights, and this one doesn't?"
Some mothers ensure rights by adopting their child as a stepchild, but the process is costly, takes years and involves invasive interviews by social services.
In Rome, Chiara says she will not consider adoption, both out of principle and the fear her sons would be at risk for too long.
She and Christine are instead readying for their move abroad, tackling bureaucratic hurdles to ensure both will be put on the baby's birth certificate.
"There are a series of highly stressful things that have to be done in a certain time -- because if not, your son won't be your son," Chiara said.
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