Is the wife entitled to spend the night outside the marital home, in the house of her sister's husband, who is not a mahram to her, for this entire period? And what is a divorce in absentia in Qatar, what are its procedures, and is the wife entitled to claim her rights, such as alimony, solace payment, and deferred mahr, in the case of a divorce in absentia?

A wife leaving her husband's home without his permission for no valid reason is considered sinful disobedience (nushuz) and is forbidden. What your wife did by leaving for her sister's house without a legitimate reason is forbidden, and she does not have the right to prevent you from managing your own money. We advise you not to hasten to divorce her. Instead, try to bring her back to her senses with your help or the help of her guardian. If she insists on not returning, then there is no blame upon you for divorcing her, and uttering the word of divorce is sufficient for that. Her divorce does not nullify her right to her deferred dower (mu'akhkhar al-sadaq), but it does nullify her right to maintenance, clothing, and housing. You may leave her in a state of suspension until she ransoms herself from you with money, as long as she persists in her disobedience. As for official divorce procedures and the consolatory gift (mut'ah) for the divorced woman, specialists should be consulted. The consolatory gift is recommended and not obligatory except in specific cases.