Zakāh cannot be channeled towards the madrasah fees of children where their maintenance, according to the rules of nafaqah, devolves upon a relative. The absence of the father does not necessarily render the children destitute, since in terms of the rules of nafaqah, their maintenance, if not already taken care of by income deriving from the father’s properties, devolves upon other relatives.
The child’s status is that he/she is makfiyy al-nafaqah, and as such cannot be spoken of in terms of faqr or maskanah, which are the only factors that come into play in this regard.
Yes, if the person responsible for the child’s nafaqah himself qualifies to be categorised as a faqīr or miskīn, zakāh may be given to him from which he might then pay the child’s fees, since the fees would then be regarded as part of his expenses.
And Allah taʿālā knows best.
قال الشمس الرملي في نهاية المحتاج شرح المنهاج 6/154: (والمكفي بنفقة قريب) أصل أو فرع … (ليس فقيرا) ولا مسكينا (في الأصح) لاستغنائه.