Is it permissible for a mother to donate half of her shop's rent—which she vowed to donate annually on behalf of her parents—to her children, given that one of them is a university student receiving a stipend and the other has no income?

If one vows to give a charity of money but does not specify the recipients, it should be given to the poor and the needy, because a vowed charity has the same ruling as zakat. Therefore, it is not permissible to give it to the vow-maker's ascendants, descendants, or anyone whose maintenance is obligatory upon them. Two cases are exempted from this:

First: If the vow-maker is not obligated to maintain their ascendants and descendants (either due to their inability or because someone else provides for them), then it is permissible for them to give to them if they are poor.

Second: If the relative is in debt, it is permissible to give it to them.

Based on this, it is not permissible for your mother to give the vowed charity to you unless you are poor and your maintenance is not obligatory upon her.