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, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
Indeed, you have done well by advising your husband and reminding him about observing the prayer at its prescribed fixed time. Hence, we advise you to continue admonishing him and clarifying to him the importance of the prayer and the seriousness of neglecting it, but this should be done with wisdom and fair preaching.
If there are trustworthy and rational people whom you hope that they may influence him, then you should seek their help in trying to rectify him. Besides, you should supplicate Allaah to enable him to repent and to rectify him. Then, if he becomes steadfast on righteousness, praise be to Allaah, otherwise it is better to separate from him and ask him for divorce as there is no good in keeping marital relationship with such a husband. For more benefit, please refer to Fataawa 88932 and 88016.
On the other hand, you are not Islamically obliged to agree that his children from another wife would reside with you at home.
As regards these children's religion, if they have not yet reached the age of puberty, they are considered as Muslims as they follow the religion of their father because the children follow the parent who has the best religion as clarified in Fatwa 81957.
Finally, you should advise your husband to be keen on nurturing the children according to the principles of Islam.
Allaah Knows best.