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.
This depends on the custom between you and your husband in such matters, that is, in regard to the money he provides. If it is known that your husband wants you to save it for certain types or a certain amount of needs and does not mind that you use the money that is left over afterwards, then there is no harm in disposing of the remainder of the money - after saving it – in any permissible manner, including if you help your family, which is one of the best offerings to Allaah, as it is an act of both charity and kindness to kin.
Salmaan ibn ‘Aamir Adh-Dhabbi narrated that the Prophet said: "An act of charity on a poor person is only (counted as) charity, while an act of charity on a relative is (counted as) an act of charity and maintaining ties of kinship." [Ahmad, An-Nasaa'i, At-Tirmithi and Ibn Maajah] In this case, you may dispose of the money without informing your husband.
As regards working, it is permissible for you to work provided that the work does not involve any Sharee'ah violations, and provided that your husband gives you permission to work. Indeed, you are not allowed to work without his permission as long as he provides sufficiently for you. However, if you set a condition on him to work before you got married to him, then he is obliged to fulfill this condition. For more benefit, please refer to Fataawa 82399 and 83629.
In case your husband does not give you permission to go out to work, then you can find a way to work from home and earn some money to help your family. For more benefit, kindly refer to Fataawa 86272 and 86182.
Allaah Knows best.