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. We ask Allaah to exalt his mention as well as that of his family and all his companions.
The most serious thing which the questioner mentioned about her husband is that he does not perform the daily prayers. Abandoning the prayers is an act which takes the person out of the fold of Islam according to the view of many scholars as clarified in Fatwa 84235.
Therefore, we advise you to endeavour to rectify your husband and be steadfast in advising him and reminding him of his religious obligations, like performing the prayer, spending on his wife and children and dealing with his wife kindly.
Two righteous and pious men, who are just and have religious knowledge, one from your family and another from his family, should be appointed to judge between you and look into the reasons of dispute between you. They should remind your husband about his religious obligations, especially the prayer. Allaah Says (what means): {If you fear a breach between them twain (the man and his wife), appoint (two) arbitrators, one from his family and the other from hers; If they both desire reconciliation, Allaah will cause it between them. Indeed Allaah is Ever All-Knower, Well-Acquainted with all things.}[Quran 4:35].
If your husband does not listen to the advice and persists in abandoning the prayer, and continues to be negligent regarding his obligation of spending on you and his child, and is not treating you kindly, then you may ask for divorce especially if he persists in abandoning the prayer, as there is no good for you in staying with a husband who is negligent about the greatest religious obligation after the two testimonies of faith.
If he refuses to divorce you, you may take the matter to an Islamic court in order to prove the harm which is caused to you by him, then your husband will be forced by law either to divorce you or to live with you honourably.
For more benefit on how to deal with a husband who does not perform the prayers, please refer to Fataawa 88016 and 88932, and Fatwa 83607 on the preconditions that must be fulfilled in order for work to be permissible for a woman.
Allaah Knows best.