I see it this way...
Man calls police to complain about separated wife taking property from house.
Police show up, acknowledge the civil dispute over property, and tell her to take a walk since she has established another residence... though they would likely allow her to take anything that the man does not dispute.
If she refuses then she may be arrested for obstruction/delaying, and if she forced entry maybe some type of criminal trespass or burglary. I couldn't say what statue since its Canada. If the man pushes the issue of her taking property that does not belong to her or for damage from forced entry, then there may be vandalism/theft charges as well.
That doesn't mean the charges would stick... but it would be in her best interest to avoid such a situation and bring the issue to court first.
Her name on the mortgage only entitles her to a payout when the house is sold, and a judge decides who gets what property. The house isn't hers to enter and take property any time she wants... not after a year of absence anyway.
It would be a whole lot simpler with a restraining order filed that compels her to stay away from the property.
Now... if the question were "can she move back in any time she wants?"... that is a little different since they apparently are still legally married and not legally separated. In that case her intent is not to take property.
As it is presented here, the woman would be circumventing the court and entering a residence she does not live in to take property. I would be more than happy to arrest her for it if necessary, and let her go explain to a judge why she felt it was okay to come take property from a home she does not live in.