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 ask Allaah to facilitate your matter and bless you with a pious husband and righteous children who would be a comfort of your eyes.
We advise you to be attached to Allaah and supplicate Him earnestly as much as possible; Allaah Says (what means): {And when My servants ask you, [O Muhammad], concerning Me-indeed I am near. I respond to the invocation of the supplicant when he calls upon Me.}[Quran 2:186]
Also, you should know that correspondence – in the manner which you mentioned in the question – between a woman and a non-Mahram man is not permissible, so you are obliged to repent from that. For more benefit on the prohibition of establishing an affectionate relationship between the sexes before marriage, please refer to Fatwa 81356. Nonetheless, it is permissible to wish that that young man will marry you and you may endeavor to this effect provided the religious etiquettes are met.
As regards the family of that young man objecting to him marrying you, then if this is due to the situation of your father or the work of your mother, then they should not do so. The Prophet married Safiyyah bint Huyayy ibn Akhtab whose father was the leader of the Jews of Banu An-Nadheer and he was one of the war chiefs who allied against the Prophet in the battle of Al-Khandaq (the Trench) and other battles. Moreover, the companions married some female companions whose fathers were non-Muslims, let alone being a Muslim and somehow dissolute (like your father). Besides, it is permissible for a woman to work as long as her work is permissible (abides by the Sharee’ah regulations).
Indeed, a person who is in the same situation like your mother should be praised as she is endeavoring to earn a living in order to support her children instead of earning by asking people for help and so forth.
However, that young man should endeavor to convince his parents to give their consent to his marriage to you. If they are convinced, praise be to Allaah, otherwise, in principle, he should obey them because he is obliged to obey them whereas marrying you is not an obligation on him. Of course, this is provided that he does not fear to be tempted by not marrying you, otherwise he is permitted to marry you because it is not an obligation to obey the parents in what causes harm to the son. For more benefit on the limits of obedience to parents, please refer to Fatwa 84942.
Finally, if we presume that he does not marry you for any reason, then there are many other men that you can marry. It might be that a harm is repelled from you by not marrying him; Allaah Says (what means): {Perhaps you dislike a thing and Allaah makes therein much good.}[Quran 4:19]