Slight Overreaction

I am shocked to read Ferdinand's reaction. I knew that he and the Cardinal would be upset, but Ferdinand is taking it to a level of betrayal and pure rage, "I could kill her now" (II.v.64).
"I would have their bodies burnt in a coalpit..." (II.v.68). Is he so upset that he would go to the extremes of murdering his own sister? They both are angry, but even the Cardinal has a surprised reaction to his brother, "Are you stark mad?" (II.v.67). Perhaps Ferdinand is more upset that the Duchess has gone against her word and their wishes. It looks as if he wants to keep control over his sister, preventing any other male figure in her life such as a husband or lover. It will be interesting to see the search for the identity of the father play out.