I have no idea how the USA law works now, but when I was at school in the USA(80s), my BF, had an english mother, who spent every penny, trying to get her children back or get access to them,
my friend and her brother who were born there, (it was the day after the birth of the second, he set in progress legal action to stop the children leaving) , were never allowed to back to this country,
she use to come to my house to make secret phone calls to her mum, she never met her grandparents, they died before she visited this country when she was 22,(without her dad knowing) it was incredibly sad.
Their father had insisted their mother came to the states to give birth, she never managed to get them home again, he caused endless problems with her visiting , and my friend(and brother) grew up without her mum. On quite a few occasions she was denied entry to the states, as he had legal proceeding in progress. Both her and her brother have really suffered because of this.
She needs expert advice. but the simplest way of keeping control of her child is to have it here, it will still be able to get a USA passport, but will have UK law on its side.
and if she does give birth in hospital there, she would be responsible for the astronomical costs, so if they then chose not to pay, they could use that as a way of criminalise her, no insurance company will touch her for this trip,
Hideous situation , I hope she sees sense, and has the baby here,
If there was anything wrong with the birth, her or the baby the medical costs will cripple her for life.