Is it permissible to contract an 'urfi marriage with a divorced woman, whose family and guardian refuse to marry her off, in the presence of a lawyer and witnesses, knowing that she is a custodian of children and fears that if her husband finds out, she will lose custody?

Marriage without a guardian (wali) is not permissible, and such a marriage is invalid according to the majority of scholars. If the woman's guardian is preventing her marriage (acting as an 'adil), she may refer her case to a judge. It is not permissible for a custodial mother to conceal her marriage in order to maintain custody when there is another person entitled to custody who is requesting it.