As others have said, it's probably best to do the theory training first before you go on holiday so that she can concentrate on the practical side.
But I'm not so sure what benefit there would be in doing any practical training in the UK.
"probably not the far east (DH isn’t keen) but wondering if anyone’s done it in the Caribbean or Mexico - or has any other suggestions."
If you have the funds then can I suggest Hawaii? Great diving and lots of good dive centres where you can get certified.
Otherwise look at the islands in the Mediterranean (eg Cyprus, Mallorca) or the Costa Brava in Spain (north-east coast, north of Barcelona).
"probably not the far east..."
Despite this, may I make a suggestion in the Far East? Japan.
Either Japan itself or Okinawa (definitely Okinawa as first choice, it's a Japanese island about 1,000 miles south of Tokyo). There are very good English-speaking dive centres there and both Okinawa and Japan are lovely places to visit.
Just a small point, but there are also other organisations similar to PADI. If you go to the US or some other countries then you may come across them, eg NAUI.
You can get a certification with one organisation and then do further certifications with a different organisation. They all recognise each other's certificates.