How should we act towards our poor paternal aunt who lives with her lazy ex-husband, knowing that any money we give her will reach his hands? Would that be cooperation in sin or charity?

There is no harm in giving charity to a poor paternal aunt, whether it is voluntary or obligatory charity, even if she spends this money on her ex-husband. However, if spending on her aids her in a sin (such as her continuing an illicit relationship with her ex-husband), then it is not permissible to spend on her until she repents. Both of them must be advised to repent. Likewise, it is not permissible for a man to cohabit with his irrevocably divorced wife in the same house unless each has independent facilities. Furthermore, a Muslim cannot be accused of adultery without clear proof.