The DSG gearbox as fitted to the Golf and Leon drives really well and doesn't hit economy HOWEVER search this and other sites and you'll discover it's prone to expensive problems. At £10k /3-4 years old you're at risk of buying someone's problem car

A few stage left suggestions:-

1)Toyota Prius/Auris hybrid - expensive used but incredibly reliable with very good real life economy ( I know two people running these and they get about 60mpg )

2) Your previous car was a C3 (small) - how about previous model (up to 2012) Nissan Note 1.6 auto - very reliable traditional auto with lock up and overdrive - (Yet again A friend of mine is on his third - all have been reliable and real life economy better that expected - 40+mpg). At the end of this model there were some great good value high speced models around (satnav, leather etc...)

3) Hyundai i30 auto (Petrol or Diesel) - good value using a reliable auto gearbox and on your budget you can buy with a few years manufacture's warranty still to run

Like Big John, I was thinking that a Toyota hybrid would suit. The Yaris is C3-size but the hybridf may not give the sort of performance that she wants. The Auris isn't all that much bigger and is well worth a look.

Nissan Note also a good idea. I think this has a proper automatic transmission; small Toyotas other than hybrids have a semi-automatic contraption which will only give grief.

We have the previous model of i30. Six years old now and perfectly reliable. Recommended.