I believe the original concept was going to be that Tom was intimate with Sonny's widow. That was evidently dropped. I guess it was enough to have Tom be unfaithful and Michael finding out about it and using it against him. It sort of emphasized that Michael had no compunctions about trying to hurt his stepbrother any way he could.

Why would Tom have a mistress? The same as any other man. I always thought that Vito and Michael were atypical among their peers in their faithfulness and disdain for temptations.

"When the snows fall and the white winds blow, the lone wolf dies but the pack survives."
Winter is Coming

Now this is the Law of the Jungle—as old and as true as the sky; And the wolf that shall keep it may prosper, but the wolf that shall break it must die.
As the creeper that girdles the tree-trunk, the Law runneth forward and back; For the strength of the Pack is the Wolf, and the strength of the Wolf is the Pack.