I agree that Berlin is much cheaper than Frankfurt.
There are lots of English language schools in Berlin that frequently look for native speakers. (For one I could give you a contact - my husband used to work there, but I don't know whether they are looking for teachers right now.) All in all, I think your chances are quite good. You also don't need a work permit as a EEA national. You don't have to, but it could be advantageous to get a 'Freizuegigkeitsbescheinigung' from the Auslaenderbehoerde for you. It's just a paper stating that you live in Germany exercising treaty rights. As far as I heard, it's a fairly quick over-the-counter affair.
I don't know about the job prospects for your wife, but I think she should be eligible for an 'Eingliederungskurs', a German language and culture intensive course for new immigrants. I recently also saw that the Berlin authorities offer a programme that combines a language course with work experience in Berlin companies. That could also help to gain experience and get some contacts and references.