Is it permissible to give a portion of Zakat to a sister to help her with the expenses of a computer course to improve her income, knowing that she works to help her husband with the household and children's expenses?

It is permissible to give an needy sister from zakat (definition) if she is poor and her husband does not provide sufficiently for her needs, in order to cover the costs of a course she requires. This is because she falls under the categories of zakat recipients mentioned in the verse from Surat At-Tawbah (definition): "Indeed, [prescribed] charitable donations are only to be given to the poor and the needy, and to those who work on [collecting] them, and to those whose hearts are to be reconciled, and to [free] captives and debtors, and for the cause of Allah, and to the wayfarer; [this is] an obligation from Allah. And Allah is All-Knowing, All-Wise."