<In context, it's clear that external circumstances have constrained the single mothers to return to work, e.g. "Some have to go back to work out of financial necessity only two or three months after their babies are born." >
Yes, that's showing external pressure.
<Clearly, the speaker (in this case, the BBC journalist) did not oblige Annette Cowley to return to work. So "must" in the original sentence is wrong, according to Thompson-Palmer. >
Do you know how journalist's report what was said by their interviewees?
?Single mothers must go to work, according to a government edict published today.
Single mothers must go to work, according to Anne Cowley, a mother interviewed today.
*Single mothers must go to work, according to me, the journalist.
Single mothers must go to work, if they are to survive. (according to...?)
Single mothers feel compelled to go to work. (Anne's word's, or the journalist's?)
So, no clearly about it, you are also speculating. My speculation is based on how reporters report the words of their interviewees.
<Now we know that returning to work isn't an obligation imposed by the subject: Annette goes back to work because of "financial necessity".>
If you keep fixing your head on imposed obligation, you'll get nowhere. Deontic modality can express real or assumed obligation, permission and necessity.
Annette to journalist: " Out of necessity, I must work."
?Annette to journalist: " I must work, the government says so." (Poor use of the modal from a BE standpoint.)
Annette to journalist: " I have to work, the government says so." (Good use of the modal from a BE standpoint.)
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<In context, it's clear that external circumstances have constrained the single mothers to return to work, e.g. "Some have to go back to work out of financial necessity only two or three months after their babies are born." >
Again, there are many viewpoints in one story. A journalist gathers information from various sources.
In the article, I believe that the journalist is either reporting Anne's words in a semi-direct fashion (i.e. objectivised deontic modality) or is expressing his her own conclusion of the interview.
In another part, he/she is stating (or is quoting the words of another journalist) that women have to go to work. So, if the writer of the article is Aminatta Forna, why he/she used "must" in one part of the article, and "have to" in another part to talk about the same situation.