First I suggest you establish if your Father and you are joint tenants or tenants in common. This has nothing to do with tenancies and I apologise if you know the difference:
Joint tenants pass their share of a property onto the other at death.
Tenants in common own a share of the house, not necessarily an equal share and can sell their share or on their death can leave their share to whomever they choose in their will or under the law of intestacy.
So your Father could leave his share of the property to his friend if he is a tenant in common with you, if it passes or is left to you, you will become the sole owner and could ask his friend to leave. If she refused, which would seem unlikely in the circumstances described, you may need to get a court order to make her leave, I doubt the police will show a lot of interest as they will probably claim it is a civil matter