As far as secular marriage laws interacting with Halacha, suppose the following scenario. A Teimani or Sefardic couple get married Kdas Moshe V’Yisroel. But they never get any civil marriage license in NY (or NJ). Later the husband marries another wife Kdas Moshe V’Yisroel and again never files for a civil marriage license.
Is either or both marriages legally recognized as valid under secular law?