Is it permissible for the wife's family to request her abandonment and the annulment of the marriage without cause, knowing that the husband is still awaiting the civil divorce ruling from his first wife, and he has [already] married the other girl Islamically?

It is not permissible for a woman or her family to request a divorce without a valid reason, and separating a husband and wife is considered a grave sin. If the reason for the request is the delay in consummation, and this delay was agreed upon or is customarily understood, then they are not permitted to request a divorce. However, if there was no agreement, then they have the right to request consummation or a divorce after four months from the marriage contract, and the annulment must be by a judge's ruling.