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.
If this woman abandoned the prayer as you mentioned and she does not wear Hijab and mistreats you, then she is disobedient to her Lord and negligent about the rights of her husband. So she is a disobedient wife, so you should take the steps which are determined by Allaah in treating a disobedient woman; and this is clarified in Fatwa 89480, so please refer to it.
If she becomes righteous and rectifies herself, then all perfect praise be to Allaah, otherwise it is more appropriate to divorce her as long as she is on this situation, but she has no right in fostering the children as she is a dissolute person. But if you think that you will be patient with her in order to achieve some benefits, like fearing that she will take the children and influence them with regard to their religion and moral conduct, or you fear that she will apostate and so forth, then you may keep her. Anyway, you should balance between the two matters [divorcing her and keeping her].
Finally, the following matters should be noted:
1. Fornication (or adultery) is one of the great major sins, whoever committed it is obliged to repent and avoid any means which may lead him to commit the same sin again.
2. It is permitted in Islam to marry up to four wives, so you are permitted to marry another woman even if you keep this wife, provided you are just between them.
3. Abortion is forbidden either before the soul is breathed into the foetus of after it is breathed according to the most preponderant opinion of the scholars. Abortion is even more forbidden after the soul is breathed into the foetus. Whoever took part in the process of abortion is obliged to repent. If abortion took place after the soul is breathed into the foetus, the person who carried out the abortion should pay a Diyyah (i.e. blood money), which is one-tenth of the Diyyah of the mother (i.e. 5 camels). The scholars differed in opinion with regard to the obligation of expiating for abortion, but in order to be on the safe side, it is better to pay it.
To conclude, it should be noted that the sin, or the Diyyah, or the expiation are not dropped from the mother just because she was obliged by her husband to do so.
For more benefit, please refer to Fataawa 85943 and 85558.
Allaah Knows best.