Whoever does not pray is a Disbeliever

Question :

My problem may be summarized as follows: My husband is an alcoholic and he does not pray, nor does he fast the month of Ramadhan, and he has been unemployed for a year. I have two boys from him, neither of whom has yet reached adulthood. Now I am in the house of my family and my husband is trying to persuade me to return to his home by all means and I am undecided about returning to him because of my children - should I return to him? Or should I seek a divorce, because I heard that it is not permissible to live with a person who does not pray and drinks alcohol? So what should I do? Please advise me, and may Allah reward you with goodness.

Answer:

A husband who does not pray is a disbeliever, according to the words of the Prophet:

The covenant which is between us and them is the prayer, and whoever abandoned it, has disbelieved.

And his words:
"Between a man and disbelief and Shirk is abandoning the prayer.

Whether or not he denies its obligation. If he does deny its obligation, he is a disbeliever according to the consensus of scholars. And if he abandons it due to negligence and laziness, but does not deny its obligation, he is (also) a disbeliever according to the most authoritative sayings of the scholars, based upon the two aforementioned Hadiths and other reports which carry the same meaning.

It is not permissible for you, O questioner to return to your husband, until he turns to Allah, the Most Glorified in repentance and guards strictly the prayer. May Allah guide him and grant him sincere repentance. And Allah is the Granter of success.

Source:
Ibn Baz
Fatawa Islamiyah, Vol. 2 Pages 370-371