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.
If your husband mistreats you and does not support your children as described in the question, then he indeed bears a sin for that. Islam commands the husband to treat his wife kindly, be a good companion to her, and provide for her and his children. This was previously stated with evidence in fataawa 86618, 88304 and 85012.
The fact that you are kind to him and he mistreats you indicates his meanness and harshness; the noble person acknowledges the favors and acts of kindness of others. The Prophet said, "If anyone does you a favor, recompense him, but if you do not have the means and cannot afford to recompense him, then supplicate Allaah for him until you know that you have recompensed him." [Abu Daawood]
If you hate your husband and fear neglecting his rights over you, then you are entitled to request a divorce or Khulʻ (divorce at the instance of the wife and payable by her). However, it is advised that you do not hastily opt for that solution since you have been blessed with children from him. The harms that children suffer when their parents divorce are no secret. Hence, you are advised to adhere to patience, kindly advice him, seek the mediation of wise and pious people, and supplicate Allaah to bless him with guidance. Hopefully, his attitude will be rectified and the problem will cease to exist.
If divorce or khulʻ actually takes place, how would you know for sure that the other man would marry you or that you would be happy with him? A marriage may be founded on love but eventually turn into a living hell! A person may seem nice and pleasant before marriage and then his true nature of harshness and cruelty become apparent afterwards. The point is that you should wait and not hasten to take such a decision until you fully realize what is best for you and most likely brings about favorable results.
Lastly, it should be highlighted that it is impermissible for a Muslim man to turn a wife against her husband, enticing her to get a divorce in order to marry her. The Islamic sharee'ah strictly prohibits such an act, as underlined in fatwa 92056. Some Muslim jurists even put greater emphasis on the matter and held the marriage of a man with a woman whom he turned against her husband invalid. This should be borne in mind.
Allaah knows best.