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The key issue is whether "exclusive use and possession" means that the house can be titled in your name alone?
If so, then you would have the same rights as any landlord to evict a tenant (you would need to refer to local landlord-tenant regulations in the place you live). If not, then enforcement may require asking the judge who is handling the case to issue an order to the ex to vacate the premises. If there is any physical threat issued by the ex in response to a request to leave, it would be possible to then get a court to issue a restraining order
("protective order") that would force him to stay a certain distance away from you and the house or go to jail for contempt of court.
In any case, a recalcitrant ex can get his own lawyer and fight. So if there is a some collaborative means to make things happen (perhaps a separate written agreement on a date to vacate), then that is best thing.
The emotions surrounding divorce often make resolution of issues more difficult -- so it is really important to get everyone, if possible, to agree on things. While it may be possible to use the law if needed as a kind of cudgel, getting people to agree and subsist in a safe emotional space is the best route -- if possible (we all know that some people are simply ruled by emotion regardless of the logic of their positions).
I wish you all the best as you move forward -- and offer best wishes for happy new year!