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, sallallaahu ʻalayhi wa sallam, is His slave and Messenger.
It is an obligation on your husband to provide for you and your daughter. You are not obliged to provide for yourself or your child, even if you are rich. Allaah, The Exalted, says (what means): {Let a man of wealth spend from his wealth, and he whose provision is restricted - let him spend from what Allaah has given him. Allaah does not charge a soul except (according to) what He has given it...} [Quran 65:7]
Hence, your husband should strive to earn a living in order to provide for you and your child. If he neglects this religious obligation, then he bears a sin for his negligence. The Hanbali scholar Ar-Ruhaybaani cited the following statement from Ar-Riʻaayah (a Hanbali Fiqh book), “It is an obligation on the one who neither has an income nor whose dependents have an income to earn a living...” [Mataalib Uli An-Nuha]
What you have spent on yourself and your daughter, if you did not spend it as a donation (gift), then you have the right to ask your husband to repay all the money that you have spent, as we have previously underlined in fatwa 85012. If you have spent the money with the intention of giving a donation, then you will be rewarded for that, Allaah willing.
As for your husband's request for your financial help to start his business, if you believe that he is diligent and trustworthy, then helping him would be a good thing. You can also offer to be his partner in this business. It is better if you consult those who know your husband and his competence in this field and perform the Istikhaarah prayer (guidance-seeking prayer). Please refer to fatwa 81434 about the manner of performing the Istikhaarah prayer.
Taking a second wife is allowed, in principle, for the man who is able to be just among his wives. However, some scholars held that a man who is unable to provide for his wife should be forbidden from taking a second wife unless he fears that he will suffer harm (if he did not marry again). Al-Kharashi wrote in his commentary on Mukhtasar Khaleel (a Maaliki book of Fiqh) about the ruling on marriage, “It (marriage) is prohibited for a man who does not fear temptation (committing adultery) and who would harm his wife by being unable to provide for her...”
On the other hand, your husband wronged you by expressing his hatred towards you; this is contrary to the enjoined kindness among the spouses. Allaah, The Exalted, says (what means): {...And live with them in kindness. For if you dislike them - perhaps you dislike a thing and Allaah makes therein much good.} [Quran 4:19]
You said that your husband “continually speaks with her, but they do not live together.” If you mean that he does not live with her and thus does not observe justice between you and his other wife with regards to the overnight stay, then this is injustice. Scholars stated that the husband is obliged to treat all his wives equally with regards to spending the night, even if each resides in a different country, as has been underlined in fatwa 90663.
If your husband wants to make you and his other wife live in the same house, then it is impermissible for him to do so except if you and her both agree. Ibn Qudaamah wrote, “A husband is not allowed to keep his two wives in one house without their consent.”
Lastly, we advise you to be patient and discuss the matter gently with your husband, and you both should be keen on doing everything that would preserve your family and avoid disputes or separation as that might eventually cause the breaking up of the family, and your daughter would be the victim.
Allaah knows best.