Is it permissible to distribute Zakat funds to the poor and orphans who commit sins (such as smoking and immodest dress), and is it permissible to condition the disbursement of aid on the attendance of sons and daughters at religious lessons in the mosque?

There is no harm in giving charity to sons who smoke or daughters who are immodestly dressed, as long as one is not certain that it will be used for disobedience. This might even be an incentive for them to listen to advice and repent. One must be keen to advise them and invite them to goodness with wisdom. As for obligatory Zakat (definition), it is only to be given to those eligible among the eight categories. Charity should not be withheld from women who do not bring their children, especially if they are in need, and children can be attracted to the mosque through permissible recreational programs.