Is it permissible to remain with a husband who is addicted to alcohol and smoking and does not pray, especially with ongoing problems and their impact on the children, and after numerous failed attempts to reform him?

If what you mentioned about your husband – his abandoning prayer, drinking alcohol, and smoking – is true, then he is committing grave transgressions. You must continue to advise him in a kind manner, seek the help of scholars and righteous people to distance him from bad companions, and make abundant supplication for him. If he repents and becomes upright, then that is what is desired. Otherwise, it is better for you to separate from him if you do not hope for his reform, in order to safeguard your religion, your worldly life, and the religion and morals of your children.