It is best for a Muslim to stay far away from cursing, insulting, and other traits that go against good manners and the noble qualities that a Muslim ought to be known by.
Imam Al Bukhari narrated from Anas who said: The Messenger of Allah ﷺ was not someone who used foul words, nor one who cursed, nor one who insulted.
And in al-Tirmidhi, from Salim ibn Umar, may Allah be pleased with them both, he said: The Messenger of Allah ﷺ said, “A believer is not someone who curses.”
Shayk Bin Baz said: The Sharia-based evidences show that it is not allowed for a Muslim to curse animals, whether camels, cows, or any other type. A Muslim is not allowed to curse any animal, whether it is one that can be eaten or one that cannot be eaten. The woman who cursed her she-camel, and the Prophet, peace and blessings be upon him, ordered that it be set free, the scholars mentioned that this was a form of disciplinary action so that she would not return to doing such a thing again.
Although the she-camel remained in the ownership of its owner and did not exit her possession according to the scholars, this was done as a means of discipline.
As for the cursing that occurred from your mother, if her awareness had changed and her mind was no longer sound, then there is nothing upon her, because she would no longer be held accountable due to the absence of full awareness, which happened because of her old age, and she would be considered among those who have no reasoning.
The Prophet ﷺ, said, “The pen has been lifted from three: from the one who is asleep until he wakes up, from the insane until he regains his mind” and in another wording, “from the one who is mentally incapable until he regains awareness” and from the child until he reaches puberty.
So if her mind had indeed changed, then there is no sin upon her. But if she had her mind with her at the time she uttered the curse, and she was aware and understood that this is not allowed, and she had reasoning, then she must be advised and told that this is not allowed, and that she must repent from that.
As for you, you are not harmed by this. Your sheep and your wealth are not harmed by her cursing them, and there is no blame on you for using them, eating from them, or drinking from their milk. There is no harm on you, because you are the one who has been wronged, and the sin is upon the one who cursed.
The sin is upon her, if she was mentally aware. But if her mind had gone due to old age, then there is nothing upon her. There is no sin upon her, and her words carry no value and are considered void. (click here to see the fatwa from his website)
‘Imran b. Husain reported: We were with Allah’s Messenger (ﷺ) in some of his journeys a woman from the Ansar was riding a she-camel. She became irritated, so she cursed the camel. The Messenger of Allah ﷺ heard this and said, “Take what is on her and leave her, for she is cursed.” Imran said: It is as if I can see her now, walking among the people and no one interfering with her.
Reference: Sahih Muslim 2595a

An Nawawi said: His ﷺ statement regarding the she-camel that the woman had cursed, “Take what is on her and leave her, for she is cursed,” and in another narration, “A she-camel bearing a curse will not accompany us,” was said as a means of reprimanding her and warning others as well.
The woman had already previously been forbidden, as had others, from cursing, so she was punished by being deprived of the she-camel. What is meant is the prohibition of accompanying that cursed she-camel along the road.
Sharh Sahih Muslim By An Nawawi (16/147)

9522 – Yahya narrated to us, from Ibn Ajnan, who said: I heard my father narrating from Abu Hurayrah, who said: The Prophet ﷺ was on a journey and moving along, and a man cursed a she-camel. So the Prophet said, “Where is the owner of the she-camel?” The man said, “I am.” He said, “Take her aside, for she has been responded to in it.”
Footenote from Shauyb Al Arnaut: This hadith is authentic due to supporting evidence, and this chain is good. Ibn Ajnan, who is Muhammad, and his father are both truthful. It was also reported by al-Nasai in al-Kubra (8815), and from him by al-Tahawi in Sharh Mushkil al-Athar (3540) through the route of al-Layth ibn Saad, and by al-Khara’iti in Makarim al-Akhlaq (73) through the route of Humayd ibn al-Aswad, both of them from Ibn Ajnan with this same chain.
And there are other narrations in this chapter from Abu Barzah al-Aslami, which will come in (4/420), and from Imran ibn Husayn which will come in (4/429) and (4/431), and from Aishah the Mother of the Believers, which will come in (6/138), and from Jabir ibn Abdillah as recorded by Muslim (3009), Abu Dawud (1532), al-Tahawi in Sharh Mushkil al-Athar (3539), and Ibn Hibban (5742). This is an authentic hadith, and this chain is good.
Musnad Ahmad (15/320)
Shayk Fawzan says: It is not permissible to curse animals at all, whether they are riding animals, or cattle, or any other type of creature. This is because cursing is a harmful and severe word, and a believer should not be someone who curses. Instead, they should use good and kind speech.
