Praise be to Allah, and peace and blessings be upon the Messenger of Allah and his family.
Firstly:
If your mother left gold with you on the basis that you would give it to your brother after she died because he needed it, then this is a bequest, and a bequest to an heir is not valid unless the other heirs agree to it.
If the heirs are adults of sound mind, and they agreed to the bequest after your mother’s death, then the bequest may be carried out. As for your consent before her death, it is of no significance, because the gold did not come into the possession of the heirs before your mother died, so their consent before her death does not count.
Based on that, if there was consent after your mother’s death, then the bequest is valid. If they did not consent, or some consented and others did not, then the bequest is to be carried out with regard to those who agreed.
Al-Hajjaawi (may Allah have mercy on him): … unless the heirs give their consent after [the testator’s] death, then it is valid to carry out the bequest.
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said:
The phrase “after [the testator’s] death” refers to [the heirs’] consent, i.e., unless the heirs give consent after [the testator’s] death, because if they give consent before his death, that consent does not count for anything, because they had not yet taken possession of the wealth. Therefore they do not have the authority to give away any of it, because consent here is to give something away. And because the one who is the heir today may end up being the one from whom wealth is inherited (i.e., he may die earlier than the testator). It often happens that one man is healthy and another is very ill, but the former dies before the latter; so their consent does not count, unless it came after [the testator’s] death.
End quote from ash-Sharh al-Mumti‘ (11/141)
For more information, please see the answer to questions no. 106236 and 91530
Secondly:
If consent has been given and the bequest becomes valid, then this gold or other types of wealth that has been bequeathed, is a trust in the care of the one to whom it has been entrusted, whether that is you or someone else who is acting as a trustee. So it is not permissible to borrow from it or to dispose of it by selling, buying or giving, unless that is in the best interests of the owner of the wealth and will benefit him. That is if he has no authority over his wealth because he is a minor and the like. But if he is an adult of sound mind, then it is not permissible to dispose of anything of his property until one has first consulted him and asked his permission.
What you must do now is put the trust back as it was. If some of this gold has been sold, then your sister should buy some gold as a replacement for it, then put it back with the amaanah (that which has been entrusted to her keeping).
Note:
Some parents may give some wealth to one child to help him to get married, for example, then make a bequest to another child of some wealth, based on the idea of equity between the children; so just as he gave something to the older child, he thinks that he must give something to the younger. If that is not possible during his lifetime, then he makes a bequest to him after his death of something similar to what he gave to his siblings. But this is not correct, because he only gave money to one who was in need, and this younger child was not in need at that time. If he (the younger child) needs to get married and so on, then the father must also give him according to his need as he gave to his brother. But if the father dies before the younger child needs this kind of money, then there is no blame on the father, and this younger child who did not reach the stage of needing that help during his father’s lifetime is not entitled to anything.
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: Hence it is regarded as a mistake when some people arrange the marriages of those of their sons who have reached the age of marriage, and also have younger children, so they write in their wills, “I bequeath to my sons who have not yet got married that the marriage of each one should be arranged with money from one third of the estate.” This is not permissible, because arranging the marriage comes under the heading of meeting needs, and these (younger children) had not reached the age of marriage. So making a bequest to them is haraam and should not be carried out; in fact it is not permissible for the heirs to carry out this bequest, unless those of them who are adults and of sound mind give their consent to that, in which case there is nothing wrong with an heir doing that with regard to his own share of the estate.
End quote from ash-Sharh al-Mumti‘ (4/599).
And Allah knows best.