Is there a card hierarchy for when cards contradict? For example, a player in a melee game reveals the plot Sneak Attack, saying he cannot initiate more than one challenge during the Challenges Phase. He then selects the title of Hand of the King, saying he may initiate an additional power challenge during the Challenges Phase, against a different opponent.

Am I correct that these cards contradict each other? If I am correct, is there any guidance on which card takes precedence in this case?

You are correct that there is a contradiction. The answer is that "cannot" always wins. As the Rules Reference says:

Cannot
The word “cannot” is absolute, and cannot be countermanded by other abilities.

See also "Timing of Simultaneous Resolution" for examples not involving "cannot" (usually timing issues).