I think Michael may have had the opposite problem with Apollonia as he had with Kay.

Much of Michael's desire to track down and marry Kay had to do with her being a WASP. He used her as part of his plan to be accepted by the American pezzonovante.

Remember, his lifelong desire was to be considered "legitimate" (even if he wasn't).

How would Apollonia have helped with that? Would a rural Sicilian girl have the ability to drink coffee and make small talk with people like Senator Geary's wife?

She didn't seem too eager to learn English, much less to become an American society dame. I can't imagine she would have had any interest in playing the part of a successful businessman's wife.

I think, once the Thunderbolt faded, Michael would have grown very weary of Apollonia and considered her a hindrance to achieving his goals.

If that came to pass, I wonder how he would have handled it?