All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
First of all, we congratulate you upon embracing Islam and we ask Allaah to make you firm and steadfast on this religion until the day you meet Him.
If your husband is as you have stated in your question that he does not pray and he consumes intoxicants, then the least that can be said about him is that he is a dissolute person as both these sins are great major sins. This is so because some scholars are of the view that a person who abandons the prayer goes out of the fold of Islam even if he abandoned the prayer out of laziness. If on top of abandoning the prayer and consuming intoxicants, he does not fulfil the rights of his family, then the matter is more serious.
Therefore, we advise you to admonish him in a good and soft manner, and supplicate to Allaah to guide him. You may seek the help of his righteous and pious relatives; it might be that they will succeed in influencing him and he will repent and become righteous, and this is good for you and your children. However, if he continues on this state neglecting the Rights of his Lord and the rights of his wife and children, then there is no good for you in staying with him, and it is more appropriate to ask for divorce.
If he refuses to grant you divorce, then you can take the matter to an Islamic court, and Allaah will grant you with a better husband than him.
Finally, we advise you to hold fast to your religion and be keen on nurturing your children according to Islamic morals and principles, and not be influenced by the wrong that this man is inflicting on you. One should not judge Islam by the bad behaviour of some Muslims.
We ask Allaah to make you and us firm on this true religion until the day we meet Him.
Allaah Knows best.