As an EU qualified attorney, I would be very happy to answer your question.
Under Portuguese law, anyone who has been living with an unmarried or legally separated person at the time of their death for more than two years, under conditions similar to those of spouses is entitled to apply (within 2 years of death) for maintenance from the estate of the deceased if she cannot obtain maintenance from her own relatives or there aren't any.
"Maintenance" means basically everything one needs for a basic decent life (food, clothing, housing). However, even if she does go through this kind of judicial action, you may be entitled to change her residence (i.e. offer her a smaller apartment or a rental place). Make sure, however, that your father (maybe you could ask him while alive) did not sign any kind of contract with her, especially not a notarized contract, regarding the right to live in the house. Furthermore, your father might also have made a Will. If he did, he would have been entitled to leave her either a part of the house, or the right to live inside it for the rest of her life. In either case (contract or Will) she would have a document which is legally binding on the heirs (i.e. you), and which you could contest only through a Portuguese court.
What I would suggest is politely inquiring about what are her plans for the future, and explain that you will need the house for yourself, and present alternative suggestions. If you do reach an agreement with her, make sure you go to the local Portuguese notary to get it authenticated, so that nobody changes their mind afterwards.
If you do not agree and have to go to court to get her evicted, the Portuguese court closest to where the house is situated would be competent. To help you find a local notary / attorney and the specific court, you should use the portal e-justice.eu, with the options "Find a ... (lawyer / notary)" as well as the European Judicial Atlas, choosing Portugal, here: http://ec.europa.eu/justice_home/judicialatlascivil/html/cc_searchmunicipality_en.jsp#statePage0
I hope my answer helped you find your options, and I would be happy if you could accept and rate it.
Dr. Ioan-Luca Vlad