What she can afford is not the issue.
You can seek an order for sole possession.
Review your game plan with local counsel
Generally one is required to provide a roof over ones spouse's head and a spouse would have access to the marital home.
I have seen one attorney post here that in my state (PA) a spouse is not a tenant and would not be protected from that body of law form being exited from a home they did not own, They might have other rights under equity to seek a portion of the home value increase over the marriage --but not the use.
Be careful not to get into physical confrontation lest adversary claim abuse and she seek and secure a protection order which effectively bars YOU from the home