Hello everyone! I found myself in the middle of a burocratic mess, and I'm not sure what I'm suposed to do. Luckly I still have 7 months before learning everything I need. I really hope you can help me here it is:

I am portuguese, and I am married to a brazilian woman who has been living legally in Portugal for the past 4 years (first as a student, now as a EEA family member). I'm in the middle of an MA degree, and in september I will be going to Leeds to do my internship in the portuguese department of the Leeds University there. My internship will have the duration of one year. I want my wife to go with me because we don't want to be appart for one year. My wife works in an online dictionary, for a brazilian company based in Portugal, so she works from home and she can work from any country she wants (but always for the portuguese goverment) and she will not be working in the UK for the UK goverment, she will only remain working for the portuguese based company online. The thing is, I know that in order to enter the UK with me, she will need to apply for the EEA family permit, but that permit has a 6 month expiration date. We will only stay one year. If she applies for the citizen visa, it can take up to a year and they keep her passport with them preventing her from leaving the UK, but we can't do that, because if she entered the UK with a 6 months permit, and then she asked for the citizen visa, it is possible that we would have to stay in the UK for one and a half year, but my grant (for the internship) ends in the end of the one year internship.
What I wanted to know was: Can she enter the UK with the EEA family permit, and then just ask to extend the family permit for another 6 months from inside the UK? What is the best way to do this, i.e., to stay in the UK with me for one year legally, and then be able to come back to Portugal?
Thank you so much for your kind attention!