Wedding Invitations

My father is a judge. Should he use “The Honorable” in my wedding invitation?

“The Honorable” is always used when addressing a judge. However it
would appear presumptuous for him to bestow that title upon himself.
When issuing the invitation, he should use “Judge” as his title.

My mother is a judge and my father is not, how should their names read in my wedding invitation?

Just like the examples above, the most socially proper would be for
her name to appear as “Mrs.” but if she wants to use her professional
title, her name would appear on the first line preceded by “Judge.” The
second line would read, “and Mr. Stephen Andrew Sampson.” Again, the
word “and” communicates that they are married.