Breach of contract is a civil matter, not a criminal offense. The remedy is to sue, not to seek prosecution.
Nonetheless, you are admitting that Breach of Contract (including Marital Perfidy) should be referred to the Civil Courts for adjudication.
Thus, the rectitude of Theonomic Libertarianism is established, in referring only the Second Table of the Law to the general authority of the Magistrate, and the First Table to the Presbyter. (As opposed to the Reconstructionist approach of establishing State Enforcement over Both Tables of the Law).
Best, OP