Praise be to Allah.
Firstly: The woman has the right to donate some of her money without her husband’s permission
A woman has the right to donate some of her money without her husband’s permission, but she should inform him so as to maintain a good relationship, especially if a large amount of money is involved.
Al-Bukhaari (978) and Muslim (885) narrated that Jaabir ibn ‘Abdillah said: The Prophet (blessings and peace of Allah be upon him) stood one day on (Eid) al-Fitr and prayed. He started with the prayer then he delivered the khutbah. When he had finished he came down (from the minbar) and went to the women, and he exhorted them whilst leaning on Bilaal’s arm. Bilaal spread his cloak and the women threw charity into it. According to another report, he said: They started to give their jewellery in charity.
An-Nawawi (may Allah have mercy on him) said: This hadith indicates that it is permissible for a woman to give some of her wealth in charity without her husband’s permission, and that is not limited to one third of a woman’s wealth. This is our view and the view of the majority.
Malik said: It is not permissible for her to give more than one third of her wealth except with her husband’s consent.
The evidence for this from the hadith is the fact that the Prophet (blessings and peace of Allah be upon him) did not ask them whether their husbands had given permission for this or not, or whether it was more than one third or not. If that made a difference to the ruling, he would have asked them.
End quote from Sharh Muslim (6/173).
Al-Haafiz Ibn Hajar (may Allah have mercy on him) said: This hadith indicates that it is permissible for a woman to give charity from her wealth without her husband’s permission.
End quote from Fath al-Baari (1/193).
But if the wife is incompetent and does not handle money well, then her husband may prevent her from donating her wealth. This is how the majority of scholars interpreted the words of the Prophet (blessings and peace of Allah be upon him), “It is not permissible for a woman to give anything without her husband’s permission.” Narrated by Imam Ahmad in his Musnad (6643) and Abu Dawood (3547); classed as saheeh by al-Albaani in Saheeh Abi Dawood.
Secondly: his oath to divorce her in order to prevent her from giving any of her wealth to her family
If your husband swore an oath of divorce so that you would not give anything to your family, and he said “There is no need to break up the family”, then we advise you not to go against his wishes, because your giving money to your family will result in divorce taking place regardless [of his intention), according to the majority of scholars, whether your husband actually intended to divorce you or not.
The other scholarly view is that no divorce will take place in this case unless your husband intended the divorce; if he did not actually intend to divorce, then he must offer expiation for breaking his oath (kafaarat yameen).
You and your husband may follow this view. So if you think that your family are in desperate need, then speak to your husband and find out what his real intention was, and if he wanted to stop you from doing this but did not intend to divorce you, then let him allow you [to give something to your family] and offer expiation for breaking his oath.
For more information on swearing an oath using the threat of divorce, please see the answer to question no. 39941.
And Allah knows best.