So you follow the eviction process for your area. ANY question on law needs to include your general locale as laws vary by area.

Does she have a lease ? Is she paying rent ? If so , is she up to date ?

But as Scott said, you evict though housing court ( or correct local court in your area)

Does your sons former girlfriend have a vested interest,I can't imagine that an ex.. would want to spend any more time in what was once a shared home with your son, where they were once happy together,usually the person/s want to get away as far as possible due to lots of painful memories.

Could it be that she has spent a lot of money on this property i.e.. decorating,furnishings and so on,believing that the relationship was solid enough to build their future together on,therefore she would have lost everything,or perhaps she thinks that you should re-emburse her for all the improvements that have been made to the property since she has been there!

Was your son the guilty party for the break up or was it a mutual agreement? If she feels it was your sons fault then maybe she thinks... why should she move out, it's her home.

Your post does not give any details, so I am looking at the problem from various angles.

The way I see it is, if your happy to leave her there paying rent as any tenant would,then why not?
On the other hand if your son wishes to remain there once his ex.. has moved out then that's your choice,if this is the case then depending on her lease and your property laws there,it may be you could have to pay some kind of one off payment for improvements that have been made to the property whilst she has been the tenant, if she is forced to move out.

To know exactly where you stand go and seek out a property lawyer, they will give you all the information you need.