What is the ruling on an urfi marriage if the husband is already married and has children, and the wife fears her family's rejection, and it is agreed to convert it to a formal marriage after a period?

An 'urfi' marriage, if it fulfills the conditions of a valid marriage — including the guardian (wali) and witnesses — is a valid marriage. There is no harm in concealing it from the first wife and children, or from the family. However, if the condition of the guardian is not met, it is invalid. It is preferable for a woman to avoid situations of suspicion and to steer clear of anything that might lead to ill assumptions about her. If a lawful marriage is not possible, she should abandon it and pray for a righteous husband. It is permissible for a woman to seek a righteous husband.