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.
First of all, we thank and praise Allaah Who guided you to Islam and we ask Him to make you firm and steadfast on His Religion until the Day you meet Him.
We advise you to seek beneficial knowledge, perform good deeds and befriend righteous and pious women, as these are the best things that help a Muslim woman remain steadfast on her religion.
We also ask him to enable you to call your family to Islam by being a good example to them and speaking to them in a gentle manner.
As regards your question, the temporary marriage is void and forbidden as we clarified in Fatwa 82221. Indeed, an Islamic marriage has to meet some conditions and pillars to be valid, among which is the presence (and consent) of the guardian because a marriage without the consent of the guardian is invalid. For more benefit, please refer to Fatwa 83629.
Therefore, your marriage to this man is void and you are obliged to separate from him until he conducts the Islamic marriage contract with you.
On the other hand, since the members of your family are not Muslims, then it is not permissible for any one of them to be a guardian for you because it is not valid for a non-Muslim to be a guardian of a Muslim woman. Rather, it is the Muslim judge who would conduct your marriage [marry you off] as the Prophet said: “The (Muslim) ruler is a guardian for whoever has no guardian.”
In case there is no Muslim judge, then a pious Muslim man should marry you off; for more benefit, please refer to Fatwa 88488.
Moreover, you should know that it is permissible for a woman to marry a man who already has another wife, and there is no doubt that jealousy is a Fitrah (natural disposition upon which Allaah created mankind) in a woman, however, this Fitrah should not exceed the limits of religion and incur the anger of Allaah. For more benefit on how to overcome this matter, please refer to Fataawa 90132 and 86818.
However, if you fear that jealousy will lead you to neglect the limits of Allaah with your husband, then you may seek Khul’ from him if he does not agree to divorce you without compensation. You may also refrain from marrying him if the marriage contract between you and him is not yet conducted in an Islamic manner.
Allaah Knows best.