You usually only have to pay national insurance contributions if you are employed or self-employed in Great Britain or Northern Ireland, and you live here. However, there are situations in which you have to, or can choose to, pay national insurance contributions while you are working abroad.
I am a migrant worker from Portugal and work here on temporary contracts. Do I have to pay national insurance contributions in this country?
If you are from Portugal, you don't need to pay national insurance contributions, provided you hold a current certificate from your home country confirming you're paying national insurance there. This is because Portugal is one of the European Economic Area (EEA) countries. Countries in the EEA are European Union countries and Liechtenstein, Iceland and Norway.http://www.adviceguide.org.uk/index/your_money/benefits/national_insurance_contributions_and_benefits.htmShe should get NHS coverage whether or not she's working (and her son):
Anyone who is deemed to be ordinarily resident in the UK is entitled to free NHS hospital treatment in England. “Ordinarily resident” is a common law concept interpreted by the House of Lords in 1982 as someone who is living lawfully in the United Kingdom voluntarily and for settled purposes as part of the regular order of their life for the time being, with an identifiable purpose for their residence here which has a sufficient degree of continuity to be properly described as settled.
http://www.dh.gov.uk/en/Healthcare/Entitlementsandcharges/OverseasVisitors/Browsable/DH_074374Though I would have expected US Forces to be handling healthcare for them - either providing all treatment, or arranging it with local doctors and hospitals.