Is it permissible for a woman to seek divorce from a husband who mistreats and threatens her, does not pray, lies, demands her money, and does not provide for her, given her fear for the potential future of her children?

If your husband does not pray, lies, mistreats you, and threatens you with divorce, then there is no good for you in remaining with him. This is because he does not pray, and the one who abandons prayer out of laziness is considered a disbeliever according to the preponderant view of the scholars. It is not permissible for a disbeliever to marry a Muslim woman. Even if it is said that he is not a disbeliever, he is still a sinner and a transgressor. The second matter is that his mistreatment before consummation is not reassuring, as usually a husband displays his best character during this period. We advise you to leave him now, before consummation and before you have a child with him.