I think that it was her idea, but I don’t recall that he did anything to stop it. He also didn’t tell Michael, to whom he should have been loyal. In the scene where Kay tells Michael (out of cruelty and vindictiveness, imho), he is faced with the murder of his child by his wife and friend (Tom), the fact that another man (Tom) was involved with his wife in that crime, and the hatred his wife feels for him, hatred that has been growing for years.
Yes, the murder of the prostitute is another example. In some respects, Tom sometimes seems almost sociopathic, except in his relationships with the family, and that broke down when he chose Kay over Michael.