Praise be to Allah.
Firstly: Zakaah is not due on gold unless it reaches the nisaab (minimum threshold), which is 85 grams.
If these bracelets reach the nisaab, or your mother had other gold that when added to the bracelets reached the nisaab, then zakaah is due on them. If it does not reach the nisaab then no zakaah is due.
Secondly: The scholars differed as to whether zakaah is due on gold that is prepared for use (jewellery). In the answer to question no. 19901 we have stated that the more correct view is that zakaah is due on it.
If your mother did not pay zakaah on these bracelets all her life, because she asked someone who told her that it was not obligatory to pay zakaah on them, or because she did not know that it was obligatory to pay zakaah on them, then you do not have to pay zakaah for past years. But if she knew that zakaah was due on them but she did not pay it out of negligence, then you have to pay the zakaah that she did not pay in past years, because it is a duty that is owed to Allaah.
Shaykh Ibn ‘Uthaymeen was asked about a woman who did not know that it is obligatory to pay zakaah on jewellery until recently. Should she pay zakaah for past years?
He replied: What I think is that she does not have to pay zakaah for the past, because the custom in this country and what is usually stated by the Shaykhs is the well known view of Imam Ahmad (may Allaah have mercy on him), and the well known view of Imam Ahmad (may Allaah have mercy on him) is that there is no zakaah on jewellery that is prepared to be worn or lent. Based on this, she does not have to pay zakaah for the past, but she has to pay zakaah for the year in which she came to know that zakaah is to be paid on jewellery, and for future years, because the correct view that is supported by the evidence is that zakaah is due on jewellery, even if it is used. And Allaah is the Source of strength.
Majmoo’ Fataawa Ibn ‘Uthaymeen (18/142)
He was also asked about a woman who has owned some jewellery for four years; should she pay zakaah for the past years or not?
scholarly view is that it is obligatory to pay zakaah on jewellery if it
reaches the nisaab.
As for her question: does she have to pay zakaah on the past years?
The answer is that if she believed that it was obligatory to pay it, this is regarded as negligence on her part, so she has to repent to Allaah and pay zakaah for the time that has passed. If she did not believe that it was obligatory to pay zakaah on it, either because she did not know that or because she was uncertain because of the difference of opinion among the scholars concerning that, then she found out that zakaah is obligatory, then she must pay zakaah for the year in which she came to believe that zakaah is due on jewellery. End quote.
Fataawa Ibn ‘Uthaymeen (18/146)
Thirdly: In the event that you do not have to pay zakaah on these bracelets, then they are your property and you may dispose of them however you wish. You can sell them and spend the money on seeking knowledge and on other things. In the event that you do have to pay zakaah on them, then you must pay it immediately and it is not permissible for you to delay it. So either pay the zakaah from wealth other than these bracelets if you have other wealth, or sell them and pay the zakaah from the price, and the rest of the money will be yours to spend as you wish.
Fourthly: You should have hastened to pay the zakaah before the estate was divided, because zakaah is regarded as a debt, and the scholars are unanimously agreed that paying off debts should be done before the estate is divided. See question no 21271.
As you divided the estate before paying the zakaah, the zakaah is divided among all the heirs and each of you must pay part of it, according to his share of the estate. If one of you voluntarily pays all of it, that will suffice and he will have done good.
If you know that your mother did not pay zakaah on these bracelets because she did not know that it was obligatory to pay zakaah on them, or she followed a scholar who said that jewellery is not subject to zakaah, then you do not have to pay zakaah on them. But if you know that she did not pay zakaah out of negligence although she knew that it is obligatory, then you must pay the zakaah.