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.
The husband is obligated to have good marital relations with his wife as we clarified in Fataawa 88304 and 86618. He is also obligated to be just between his two wives in regard to staying overnight with them and spending on them as we clarified in Fatwa 82124.
Also, he is not permitted to prevent you from taking the car since it is yours. In any case, if what you mentioned about your husband is correct that he is not fulfilling your rights, like staying overnight with you and the like, then he is unjust and neglectful. So, we advise you to admonish him and remind him to fear Allaah in his wife and children. If his situation gets better, praise be to Allaah, but if the situation persists, you may take the matter to one of the Islamic Centers in your country so that they would remove the harm off you, either by rectifying him or by divorcing you from him.
Furthermore, a husband should not mistreat his wife and then call her to bed. ‘Abdullaah Ibn Zam’ah narrated that the Prophet said: "None of you should flog his wife as if he flogs a slave, and then have sexual intercourse with her at the end of the day." [Al-Bukhari and Muslim]
Ibn Hajar said: “In the same context, it is most unlikely to happen to a sound man that he would violently beat his wife and then he would have sexual intercourse with her during the rest of the day or night.” However, this Hadeeth does not mean that the wife is permitted to deny her husband his right in bed or else if he mistreats her; rather, she should answer his request.
As regards divorce, it does not take place unless the husband initiates it, and your separation without divorce is not considered a divorce; for more benefit, please refer to Fatwa 82732.
Besides, your husband is not permitted to act according to the police statement which implies that he has nothing to do with his wife and children. Rather, he is responsible for his children and he is also responsible for you as long as you are his wife, and it is confirmed that the Prophet said: "…and the man is a guardian of his family and will be questioned about the people under his guardianship." [Al-Bukhari and Muslim]
The Prophet also said: “It is enough a sin for a person not to provide means of sustenance to those whom he is obliged to support.” [Ahmad and Abu Daawood]
In addition to this, if what you mentioned about your brother-in-law is confirmed, that he mistreats you, then he is wrong as his behaviour has nothing to do with religion or real manliness.
Allaah Knows best.