Is the deceased's one-third [of his wealth] to be disbursed from his children's private home? And is it permissible to borrow from this one-third?

The will is executed from all that remains of the deceased's estate after settling their debts, based on the Almighty's saying: (after any bequest you may make or any debt). It is not permissible to borrow from the bequeathed one-third, because the beneficiary owns this one-third, and it is not permissible to dispose of another's property except with their permission.