EU law definitely applies to your case and if the authorities would decline to apply it, you could go to court to invoke it. In practice, the UK makes it a little more difficult that it needs to with delays and such but it does generally follow EU law. The famous court cases (Surinder Singh, Carpenter…) are about *British* citizens using EU law to circumvent the more restrictive rules that apply to them and their family. 

In practice, your wife will need to apply for an [EEA family permit](https://www.gov.uk/family-permit) and then, once in the UK, for a [UK residence card](https://www.gov.uk/apply-for-a-uk-residence-card/overview). In principle, she has a right to work in the UK without restrictions immediately and should get this visa quickly but in practice I have read reports from people who had to wait several months to actually get the permit they need to come to the UK and work.

One thing I don't know is whether your wife could enter the UK on her other visa and apply for a residence card directly.