What is the ruling of Islamic law regarding a woman's second marriage and pregnancy, without her divorce from her first husband, whose marriage was not documented, and what are the consequences for the first husband, the second husband, and the wife?

This is a complex issue that should be referred to courts or Islamic councils in Western countries, due to the multiplicity of possibilities and intertwined rights.

If her marriage to her first husband was legally valid, it remains so, and her second marriage is invalid. If the second husband was unaware that she was married and she was ignorant of the ruling, then their marriage is a shubha marriage (marriage based on misconception) which prevents the imposition of hadd punishment.

As for the child: If the second husband had intercourse with her during a period of purity when the first husband had not touched her, and she gave birth after six months or more, then the child belongs to him. If she gave birth in less than six months, the child definitively belongs to the first husband. If both had intercourse with her during the same period of purity, and she gave birth after six months or more, then qiyāfah (or laboratory analyses nowadays) should be used to determine the child's lineage.

The woman must observe an iddah (waiting period) from the second husband by giving birth if the child is his, then she returns to her first husband without a new contract.