Praise be to Allah.
Your husband is preventing you from embracing Islam, and does not want to become Muslim himself. He prefers divorce to Islam, although you have tried to persuade him of the truth to no avail. This means that this man is no good. Moreover, you say that he is bad-tempered and violent, that any improvement is only temporary, and that you do not love him at all. If this man is as you say, he is no good from either a religious or a worldly point of view, and there is no use in staying with him. Our advice to you in this case is to leave him immediately, and try hard to gain custody of your two daughters so that they may grow up in Islam. According to Islamic shareeah, in such cases custody should be awarded to the Muslim parent, because Islam should prevail, not be prevailed over.
As regards the second part of your question, and this man whom you say is a Muslim, you must make sure that he is a chaste man, not one who is immoral or corrupt. Do not establish any relationship with him before marriage. If you find out for sure that he is chaste and solidly religious, I advise you to marry him as soon as your iddah (waiting period after divorce) is over. I ask Allaah to take care of you by His mercy, to make the right thing easy for you, to help you enter this religion and to save you from kufr and its followers. Remember the story of Pharaohs wife, who was Muslim although her husband was a kaafir. Allaah said about her (interpretation of the meaning):
"And Allaah sets forth an example for those who believe, the wife of Pharaoh, when she said: My Lord! Build for me a home with You in Paradise, and save me from Pharaoh and his work, and save me from the people who are zaalimoon (polytheists, wrong-doers and disbelievers in Allaah)." [al-Tahreem 66:11]
May Allaah bless our Prophet Muhammad.