Is the promise to support the poor children of a deceased maternal uncle considered part of the reward for sponsoring an orphan, and can this expenditure be counted towards Zakat al-mal, or a portion of it?

It is permissible for the questioner to give her Zakat to her poor and orphaned maternal uncle's children, because she is not obligated to financially support them. The condition for this is that she pays them the Zakat with the intention that it is Zakat on wealth, and then she spends it on their needs. If she wishes to spend on them more than the Zakat, she will be rewarded for it, as it fulfills a commendable promise. If they do not have a guardian, she should give the Zakat to those among them who have reached maturity.