Unfortunately, she cannot just force him out if he has set up his residence there. They are married, so there is no "half of the rent", "his money" or "her money." The court views all assets as marital assets... so it does not matter what he has paid. It does matter if he has or has not been living there, in which case it becomes an eviction issue. She doesn't have the legal autority to kick him out. Though teh court will do so shortly if he doesn't go.    

Since this is a rental agreement, the house/apartment is not a marital asset, and she will ultimately get posession of the residence. BUt she might have to get a court order to do so.   

You did not say if there were children involved, but that also complicates things.

The best thing to do is just TRY to kick him out. Tell him he has to leave and get his stuff and go. The whole residence issue does not become a factor unless he refuses to go, and basically squats in her apartment, which would be very uncommon.

If he decides to squat, it is pretty simple. She just needs to file teh divorce and ask for temporary orders giving her possession of the marital residence. Once the court orders this, he will have to move out. It will be pretty automatic, and shoudl only take a couple of weeks at most to get the Order, should she need it.