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.
First of all, we congratulate you upon embracing Islam and we pray to Allaah to make you steadfast on this religion until the Day you meet Him.
As regards your question, abandoning prayers and fasting is one of the great major sins. If your husband is as you mentioned that he is neglectful about the rights of Allaah on him, then it is not strange for him to be neglectful about your rights. We advise you to be patient on him as patience is the key to much good. Therefore, this husband should be advised and it should be conveyed to him that neglecting prayers, failing to observe fasting and not fulfilling his wife's rights, is very serious. He should be advised in good and soft words. It is more appropriate that he is advised by people who could have influence on him. However, you should not forget to supplicate Allaah as much as possible to rectify his affairs and guide him to righteousness. It might be that he will repent and you will be happy with him in this world and in the Hereafter. Please refer to Fataawa 88016 and 84235 on the ruling of abandoning the prayer, and Fatwa 83368 on the ruling of not observing the fast.
However, if your husband persists on this condition, then we do not see any good in staying with him as a wife, rather it is more appropriate for you to ask him to divorce you. If he accepts your request, all perfect praise be to Allaah, otherwise take the issue to an Islamic court which will study the matter and remove the harm off you.
Finally, it should be noted that you should be keen on your religion and the religion of your children, and your husband's bad conduct and misbehaviour should not affect your religion.
Allaah Knows best.