Twelve years ago, Liz Prosser fled America with her then six-year-old daughter Tamara to avoid them being separated.
Lawyers for Mrs Prosser, 59, who lives near Tregaron in a remote region of North Wales, say she can now barely travel short distances.
The court heard she suffers from Crohn's disease, acute fibromyalgia, epilepsy and severe depression.
Separating her from her "devoted and caring husband" and sending her across the Atlantic in the custody of US marshals would result in her suffering "extreme pain" and inhuman and degrading treatment and lead to a high risk of suicide, two judges were told.
Her counsel Hugh Southey argued the allegations against her were "relatively minor" and not likely to result in a custodial sentence.
Hers was "an exceptional case" where forcing her to face trial would be disproportionate and violate her human rights.
Her condition had deteriorated during the lengthy delay in the US authorities obtaining her removal.
"The result is the pain she will suffer, and the discomfort and indignity, is worsening", said Mr Southey.
"She has already spent four-and-a-half months in custody in 1998-99 immediately after the arrest warrant was executed.
"Even if she is guilty of offending she has not walked off scot free."
Mrs Prosser is wanted for trial on allegations that, in March 1998, she abducted her daughter from her former husband at a time when the child should have been in his care.
She is also accused of fraudulently procuring 6,750 dollars (£4,512) from a former employer between August and November 1997.
Mr Southey said Mrs Prosser accepted that she took her daughter, who is 18 next month, from America unlawfully, contrary to a child custody order.
She did so because she believed she was about to be arrested and would be deported without her daughter and would lack the resources to retain custody.
Mr Southey said Tamara resided with her father in the US, but he was content for Mrs Prosser to play an active role in bringing up his daughter.
It was planned that she might attend university in Wales and live with her mother, he told Sir Anthony May, President of the Queen's Bench Division, and Mr Justice Foskett.
The fraud offences, which she denied, related to her employment shortly before she left the US. It was thought the allegations were she accepted money for advertisements placed in a magazine that she worked for when in fact the ads had not been sold.
Mr Southey told the judges that Mrs Prosser, who is wanted in Pennsylvania, suffered from a complex combination of both physical and mental conditions, and it did not appear to be disputed that she would suffer extreme pain if extradited.
"She will also suffer a very serious deterioration in her mental health that will result in her being a high suicide risk."
This would amount to degrading treatment, contrary to Article 3 of the European Convention on Human Rights and also be "an affront to fundamental humanitarian principles".
It would also violate her Article 8 right to family and personal life as she would be separated from her husband, Phillip, who acts as her carer and provides emotional support.
Mr Southey referred to the report of consultant psychiatrist Dr Wilhelm Skogstad which warned there was a serious risk that deterioration of her situation "will tip her fragile balance in a disastrous way" towards suicide.
Dr Skogstad stated: "She has two important factors that keep her going at the moment - a devoted and caring husband and the renewed contact with her daughter with the hope to be reunited with her."
Hugo Keith QC, appearing for the Home Secretary and supporting the US extradition request, said there was medical evidence suggesting that the pain Mrs Prosser was likely to suffer would not attain "the necessary degree of seriousness", or the "minimum level of severity" to engage Article 3.
A degree of exaggeration of her symptoms could not be excluded, and "extreme pain" during the extradition process could be mitigated by the use of a stretcher and analgesics.
The suffering flowing from her illnesses - even if exacerbated by extradition and trial and punishment - did not attain the minimum level of severity for Article 3, argued Mr Keith.
There had also been written assurances from the US authorities that "effective mechanisms" existed to reduce the risk of a serious deterioration of her mental health and attempts at suicide.
Mr Keith also rejected accusations that extradition would disproportionately interfere with Mrs Prosser's Article 8 right to family and personal life.
He argued that the interference had to be "exceptionally serious" before it outweighed the public interest in extradition going ahead, and Mrs Prosser's case did not fall within that category.
The judges reserved their decision to a later date.
Mrs Prosser wrote in a newspaper article a year ago: "If the extradition goes ahead, I'm not sure I'll survive the flight, let alone a court case or jail sentence.
"I always thought extradition was for terrorist suspects or major criminals, not people like me."
