Jan I think you are trying to impose a personal requirement of your own on Appolonia's character that was never intended to be there.

Naive, simple Appolonia was a perfect foil to Mikes complicity and dark secrets as he fled the murders he had committed.

Like the rugged beauty of the countryside where Mike took refuge, Appolonia was essentially part of that that same unspoiled simplicity; found on a hillside like a beautiful flower with a purple ribbon in her hair. This is why her character doesn't have significant performances or dialog.

She was part of the experience of Sicily which contrasted so totally to the ugliness that had occurred back in New York.
If you'll recall, the change in the tenor of the movie that Sicily provided was very distinct. It was a landscape of simple, uncomplicated beauty with breathtaking views and a background of ancient surroundings which provided a relief from the rest of the movie the way art often does in real life. Appolonia was a part of that experience.

The simpleness and innocence of her character also allowed the audience to sense that she was being 'taken in' by Michael; setting up the turn in the plot where eventually the ugliness that Michael was trying to hide from catches up with him and also finds her because of him.
It was innocence and beauty tragically lost in the best tradition of theater!!

I think the character of Appolonia was yet another masterful part of Coppola's work and added a dimension to Sicily that couldn't be expressed with landscapes. And allowed the audience to visit the tragedy that Michael's life was becoming in a deeper way.

It would be missing the point to get all wrapped up in being judgemntal about their relationship.