I must say I find a lot of the judgemental comments on here disturbing. As you say, people cannot know the full circumstances & should realise that.
If she goes, make sure you change the locks - even if your father has not given her a key there is a possibility that she took one & got it copied.
If she doesn't go, I doubt whether the police would be much help - this is really a civil matter not a criminal one unless your father has valid grounds for an allegation of some criminal offence. You could ring the Shelter helpline (see their website) or go to your local CAB to try & find out what can be done. However, I suspect that what has already been said is likely to be the case - only your father can tell her to go (I mean that in the legal sense - obviously you can do so & have done but she can ignore you with impunity unless your father tells her to go). This may be different if you had a tenancy agreement with your father & it contained a condition that no-one else was to live in the house without your permission.
If nothing was done & she remained long term it is quite conceivable that she would try (e.g. when your father died) to claim some right to the house. She would probably not succeed but it could cause endless problems & legal costs to overcome & get her out at that stage.