What is incumbent upon the children of the deceased to ensure that the entirety of her zakāt on her wealth, which her son used to estimate for her annually, has been paid out, knowing that she was very charitable and might have mixed zakāt with ṣadaqāt (voluntary charities)?

Children are not obligated to do anything merely because they suspect their mother's financial liability; the default is her financial innocence. However, if they become certain that she owes something she did not pay in Zakat, then many scholars hold that they are obligated to pay this amount before distributing the inheritance.