Bukhari

Hadith Commentary:
(1)
The child's mother herself is a burden upon his father because she is under his responsibility. When her own maintenance is not obligatory upon her, then how can the maintenance of the child be obligatory upon her? This is precisely why the Messenger of Allah (sallallahu alayhi wa sallam) did not command Umm Salamah (radi Allahu anha) to spend on her sons; rather, he only said that whatever you spend on them, you will certainly receive its reward.
(2)
When the maintenance of the child is not obligatory upon the mother, then it will be upon the father.
As long as he is alive, he himself will bear it; when he passes away, then it is the responsibility of his heirs to bear the expenses of the child.
And Allah knows best.

Hadith Commentary:
The permissibility of giving charity, including even wealth from zakat, to needy children has been established.

Hadith Commentary:
(1)
From these narrations, it is understood that charity and alms, whether obligatory or voluntary, can be given by a wife to her needy husband and by a mother to her destitute children, because the maintenance of the husband is not obligatory upon the wife, nor is the maintenance of the children obligatory upon the mother.
Some scholars have interpreted the charity mentioned in these ahadith as voluntary charity (nafl sadaqah), but Imam Bukhari rahimahullah has, at this point, taken it to mean zakah (obligatory alms), as is evident from the chapter heading.
The apparent wording of the hadith supports the position of Imam Bukhari rahimahullah.

(2)
In the hadith of Abu Sa‘id al-Khudri radi Allahu anhu, it is mentioned that Zaynab, the wife of Abdullah ibn Mas‘ud radi Allahu anhu, herself asked the question, and from the aforementioned hadith, it is understood that she told Bilal radi Allahu anhu. There is no contradiction between these two narrations.
It is possible that these were two separate incidents, or that she first spoke to Bilal and later herself asked the Messenger of Allah sallallahu alayhi wa sallam. However, from the wording of the hadith, it appears that these are two different events:
In one incident, the question was regarding charity, and in the other, it was merely inquired whether spending (on family) would be rewarded by Allah or not.

(3)
It should be noted that the second woman mentioned in the hadith was Zaynab radi Allahu anha, the wife of Abu Mas‘ud ‘Uqbah ibn ‘Amr al-Ansari radi Allahu anhu.
(Fath al-Bari: 3/414)

(4)
In the hadith of Umm Salamah radi Allahu anha, it is not explicitly stated that she spent on those orphan children from zakah wealth; however, it is certain that she did spend on them.
And Allah knows best.