Is it permissible for the children of the deceased to take from this money, and who are the actual rightful heirs?

The reference for determining those eligible for the funds is the owner of the funds who designated them. If his intention was the beneficiaries of zakat, then the funds may only be disbursed to them. And if the donor's condition was that the funds be disbursed to the poor, then they may not be disbursed to others. Accordingly, if the deceased's children meet the condition set by the donor, they are permitted to take from the funds; otherwise, they are not. And if the funds were intended for orphans, or students of knowledge, or similar categories, then the funds are distributed according to his intention. And if he intended specific individuals, then the funds must be disbursed to them.