Every day during the balmy late afternoons of southern China's spring, Xiao Chen takes her twin daughters to Shenzhen's central park.

Dressed in matching floral cotton dresses, Phoebe and Sarah hold hands and race through the park like excitable birds, playing until the sun disappears.

They stand out from other Chinese kids in the park — they're Eurasian, prompting occasional questions from other parents about whether they have a Western father. It's a question Xiao Chen would rather not answer. As a lesbian mother of kids who are seen as illegitimate under Chinese law, it's not something she likes to discuss with strangers in the park.

Xiao Chen became pregnant via in vitro fertilisation and gave birth to the twins overseas. In China, non-married women face tight restrictions when accessing artificial reproductive procedures.

IVF in China requires a marriage certificate, an ID card, and permission from the local Family Planning department.

Complicating things further is that the twin's biological mother is not Xiao Chen, but her wife, Winky. Their anonymous sperm donor is from the US.

Same-sex marriage is neither legal nor widely accepted in Chinese culture. Even though Shenzhen is seen as a liberal part of China, Xiao Chen and Winky face plenty of intolerance.

They want to send Phoebe and Sarah to day care, but they haven't been able to obtain a "hukou" — household registration certificate — for the twins. The certificate, widely seen as outdated, determines a child's access to education, healthcare and social benefits.

Without hukou, Phoebe and Sarah don't legally exist in China.

China's falling birth rate

China's birth rate has fallen to its lowest point since the founding of the People's Republic of China in 1949, although the government has allowed urban couples to have two children since 2016 to offset the rapidly growing ageing population. (In rural areas, parents were not subject to the one-child policy).

China's government wants more babies, but Phoebe and Sarah fall between the regulatory cracks because they have two mothers.

"Our society is still dominated by men and they do not pay enough attention to women's rights," says Xiao Chen.

Birth rates in China are still dropping despite government intervention. ( Reuters: Kim Kyung-Hoon, file )

The start of a new nightmare

Even if the twins make it to daycare, Xiao Chen fears they will face discrimination. It's a daunting prospect when they've already been through so much just to start their family.

Having been rejected by public hospitals that offered IVF, Xiao Chen and Winky found a private hospital in Beijing that didn't require all the certificates, although they still faced discrimination from nurses and doctors. Ultimately, Xiao Chen didn't get pregnant and they lost a lot of money in the process.

In late 2013, they went to Thailand. Just as they finalised preparations, they were told the Thai government had abruptly banned IVF due to a scandal involving Australian parents abandoning a surrogate baby with Down syndrome.

A few months later, they were told they could try again. They quickly flew to Bangkok and had an embryo implanted. Unfortunately, Xiao Chen caught a cold, and the embryo was not strong enough to survive. On their third attempt, the Thai doctor implanted two embryos and their persistence was rewarded with twins.

Xiao Chen and Winky later travelled to Los Angeles where they married. The twins were born in an American hospital and both mothers' names were put on the birth certificate.

The birth of twins brought Xiao Chen closer to her mother, who up until then hadn't accepted her sexuality and partnership.

"Everyone thought it was a perfect end to the story, but it wasn't," says Xiao Chen.

It started another nightmare.

Winky (left) and Xiao Chen (right) with their twin daughters Phoebe and Sarah. ( Supplied )

Single mothers pay a fine

Since the birth certificate had the names of both mothers, the Chinese embassy refused to issue travel documents for the twins because their same-sex marriage wasn't recognised in China.

With the assistance of friends and an NGO, Xiao Chen and Winky paid a significant amount of money to get the twins back to China.

In early 2016, the Chinese State Council quietly issued a new regulation that allowed parents to register "illegitimate" children to the hukou system using their birth certificate or a paternity testing certificate.

But the change didn't apply to children with two mothers named on a birth certificate.

Each province implements regulations differently. In some areas, single mothers are still required to pay a "social support fine" to obtain a legal hukou.

The fine can range from three to six times the annual average income in each city.

"I pay birth insurance each year to the national insurance system, but the public hospital told me I could not enjoy the discount like other married women because I am a single mother," says Xiao Chen.

Already it has cost the couple about 260,000 yuan ($54,500) for multiple IVF trips overseas.

With Xiao Chen now taking on the duties of a full-time mother, she says the family faces financial pressure and an uncertain future.

Still, she says "it's totally worth it."

Egg freezing or IVF treatment overseas is an expensive process out of reach for many Chinese women. ( ABC News )

'I can't wait any longer'

Egg freezing in the US costs about 85,000 yuan ($17,800) while the IVF process starts at 135,000 yuan ($28,300). It's a privilege reserved for the middle class.

Lim Li, chief executive of TrueBaby Reproductive Advisory in Shanghai, says the number of Chinese women who want to go overseas to get IVF or egg-freezing has increased by 10 per cent each year for the past four years.

"Our single female customers are aged 30 to 42. They are usually well-educated, have a good job or are in a good economic situation," he says.

An increasing number of young Chinese women are hoping the Chinese government will change the law to allow such treatment in China.

One woman, 27-year-old Beijing resident A Lan, recently wrote a letter to a deputy of the National People's Congress (NPC) to propose that all Chinese sperm banks accept applications from single women.

A Lan is looking for someone to have a baby with, without getting married. ( Supplied )

She hopes that during the congress in March, the NPC deputy could submit her proposal to China's lawmakers.

She also posted a video online looking for a sperm donor for herself.

"I don't have expectations about marriage, but I want to have a child on my own, and I can't wait any longer," says A Lan.

"I want to get pregnant in a natural way. I want to find someone who does not want to get married but desires a child so that I can share financial responsibilities as well."

She has found two potential candidates so far. She hopes to have a baby next year, but in the meantime has been talking to lawyers about the potential risks.

"If today we have more choices, the next generations will have even more diverse choices," A Lan says.

"By then, a voice will say proudly, 'my mother has fought for this'."

Protecting 'traditional values'

A Lan is not the first person to lobby for a legal change.

Yingying Zhan, a young female lawyer, sent letters to 64 NPC deputies pleading with them to allow unmarried women to have access to reproductive technologies.

Zhan has been campaigning on fertility issues along with other feminist activists for more than two years.

In 2017, NPC deputy Hairong Dai proposed amending the family planning law.

But the National Health and Family Planning Commission says the issue requires more research. In a reply to Dai posted on its website, it said "legalising single women's reproductive rights does not conform to Chinese traditional values, or public order. Restricting single women's access to reproductive technology shows protection of children's rights."

Yuan Feng, the co-founder of women's rights NGO Equality, says the policymakers fear change.

"They are worried once single women are entitled to reproductive freedom, it would massively impact the current family structure, the relations with men, and current ethical standards," Feng says.

With the pressures of a low birth rate, Feng believes policymakers will loosen the restrictions in future — but will still try to maintain some control.

For Xiao Chen, the answer is simple.

"Women's golden age to bear children is very short," she says. "I hope the Chinese government can allow single women to freeze eggs and fertilised embryos."

Cecily Huang is a producer in ABC's Beijing bureau.