Chanbua told Fairfax Media she initiated legal action in Australia in 2016 to try to have Pipah returned to live with her and Gammy in Thailand because"I kept thinking about her living with a sex offender."
She said she has now accepted a WA Family Court decision to grant custody of Pipah to the Farnells,who live in Bunbury,under strict conditions.
"But I have not given up trying to see my daughter,"she said.
WA Chief Justice Stephen Thackray found that Pipah,who had been raised by the Farnells since birth,lived a happy and contented life and would be traumatised if removed from the only parents she had known.
Justice Thackray found the Farnells lied under oath about Wendy being the eggs donor for the twins when the pair actually used an anonymous egg donor,together with David's sperm.
But Western Australia's Director of Public Prosecutions later said the state did not consider in the public interest for the Farnells to be charged with perjury.
Chanbua said she now wants to make a new appeal to the Farnells.
"Please can we meet in Australia? Or we could meet halfway,or anywhere. It's up to them,"she said
Gammy has been granted Australian citizenship,on the basis that her biological father is Australian.
Arriving home to take care of Gammy after finishing a shift at a bakery,Chanbua said she can't help thinking how Pipah's birthday would be celebrated in a country she has never visited and knows little about.
Gammy cannot speak but he is an active and mostly healthy toddler who likes dancing to music and taking selfies with his mother's mobile telephone.
"The doctors think he will speak when he is seven or eight,"Chanbua said.
"They don't seem too worried."
When Fairfax Media broke news of Gammy's plight in 2014 he was in a critical condition suffering a heart condition and other illnesses. The ensuing scandal prompted Thailand's military government to outlaw commercial surrogacy and shutdown dozens of surrogacy clinics and agencies in Bangkok.
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The story prompted Australians to donate $240,000 which has been used to buy the family a house,provide them a monthly allowance of $590 and pay for Gammy's kindergarten and hospital visits.
"It's made a big difference to his life ... you can see how happy he is,"Chanbua said.