Hi!
In order to work as a doctor, I believe your mum would have to do some kind of training/courses to convert her qualification (since Italian medicines, regulations, etc can be different from English ones). Additionally your mum would have to speak very good Italian. It is very difficult to get a job as a doctor unless you speak the language very well (I know it is different in the UK…. You have lots of doctors who are not native speakers… in Italy it is not like that). Having said that, if she gets her qualification recognized in Italy and if she speaks the language well enough, she should be able to get a job.
Not sure what kind of teaching experience/qualifications your mum has. In order to teach English in a public school she needs to be a qualified teacher (e.g. hold a teaching degree). In order to work in a language school it is often enough to be a native speaker and have a TEFL certificate or equivalent (but of course it depends on the school and it makes sense to check with several schools before moving to Italy).
An alternative would be to offer private lessons and/or conversation classes. It takes a while to establish this kind of “business” (you need to find enough students, etc.) but once you have done so it can be quite profitable.
Before your mum moves to Italy it makes sense to consider carefully where to move to! Be aware that unemployment in the South of Italy is really high at the moment… finding a job in regions such as Calabria or Puglia is nearly impossible. If she wants to teach English or give English lessons I would choose a town with a university.
If your mum does not speak any Italian at all, I would recommend that she learns at least the basics before moving to Italy. It is not easy to survive in Italy without at least a basic knowledge, as many Italians still do not speak English (especially people over 40).