It is not "illogical" for a physical law to be violated .. it is an exception that is caused by the will of G-d.
It is entirely different from making illogical statements such as Jesus is a man, but Jesus is also G-d .. and G-d created man.
Can you not see the difference?
It is true that they are deductively invalid for different reasons. The Trinity violates the Law of Identity. Miracles, as you define them, violate the Law of Noncontradiction.
For instance, there can never be a married bachelor. Once a bachelor becomes married, they are no longer a bachelor. For the same reason, we can never have a physical law that is violated because, once it is violated, it is no longer a physical law.