Well it's from the book and not the movie but when Vito was promoted to consigliere, (paraphrasing here) Tom was amused to learn that the other Families were slightly contemptuous of this move and had started calling the Corleone Family "The Irish Gang". It let Tom know that he'd never be fully accepted in the Sicilian organization and could never hope to succeed the Don.

But what's important here per the book is that Tom never had any desire to succeed the Don and viewed such an ambition as disrespectful to his "father" Vito and Vito's sons.

So even though Michael abused Tom's loyalty and treated him disrespectfully I don't think Tom ever could have had taken any action against him. At most he might have left, but as we know his loyalty (love?) wouldn't let him do that either.