Question:
Answer:
This sounds like a hypothetical question since, in the U.S. and in much of the West, polygamy is illegal. I also think it should be answered strictly as a question of what to do about polygamy in an area of the world where it is illegal rather than considering the matter of conversion to Islam (which is incidental if a spouse is engaging in illegal acts).
The Code of Canon Law states:
A spouse who occasions grave danger of soul or body to the other or to the children, or otherwise makes the common life unduly difficult, provides the other spouse with a reason to leave, either by a decree of the local ordinary or, if there is danger in delay, even on his or her own authority. In all cases, when the reason for separation ceases, the common conjugal life is to be restored, unless otherwise provided by ecclesiastical authority (canon 1153).
A woman whose husband has broken their marriage vows to remain faithful to his wife (and to her alone) for life, and who now finds herself in a situation in which her safety and the safety of minor children may be at risk, is able to leave—on her own authority, if necessary. If it is safe for her to do so, she may inform the civil authorities of her husband’s illegal activities. She may seek a civil divorce in order to protect herself and her children from him.
A bond of sacramental marriage may remain, so a woman in this situation would need to petition the Church to look at her marriage to determine if the marriage is valid and sacramental before she is free to enter another romantic relationship during her putative husband’s lifetime.