How can one deal with a husband who is passive, addicted to tobacco, and has illicit relationships with women, given the difficulty of separation due to family circumstances and the wife's aversion to him?

One of the most dangerous things you mentioned about your husband is his negligence in prayers, and this is a serious matter and one of the major sins. The first thing we advise you to do is to supplicate for your husband's guidance. Be keen to advise him gently and with kind words. If you see that someone else, whose advice you hope he will accept, can counsel him, then that is preferable. If his situation improves, then that is good and fortunate. Otherwise, living with someone like him is a trial, and if the husband abandons a right due to Allah the Almighty, then the wife is in the same position regarding that. Therefore, it is desirable for her to seek a khul' (divorce initiated by the wife) from him due to his abandonment of the rights of Allah the Almighty. Nevertheless, if you choose to be patient with him and continue advising him, there is no harm in that. Strive to console yourself by remembering Allah, reciting the Quran, and keeping good company.