What is the ruling on a husband who divorced his second wife in absentia and wants her back, but her family refuses; does she still count as his wife; and is the first wife sinful for requesting the divorce of the second wife?

The Gist of the Fatwa: Your divorce is valid and there is no issue with it. The fact that you divorced due to your wife's insistence and quarrel with you does not prevent the divorce from taking effect, as this is not considered a valid form of duress. The fact that the divorce did not take place in court does not prevent its validity. If it was less than three pronouncements and not for a financial consideration, then it is a revocable divorce (ṭalāq rajʿī) during which you have the right to take your wife back before her waiting period (iddah) expires. The wife's consent or her family's consent is not required for the revocation.

As for the ruling on your wife asking you to divorce her co-wife so that she does not compete with her: this is impermissible, due to the saying of the Messenger of Allah (peace and blessings be upon him): "It is not permissible for a woman to ask for the divorce of her sister [in Islam, meaning co-wife] in order to empty her plate (i.e., take her share), for indeed, she will only have what has been decreed for her."