To whom does the guardianship of children fall after the father's death, to the paternal uncle or to the mother?

If by "guardianship" you mean authority over the property of minor children, then neither the mother nor the paternal uncle has a right to it. Rather, it belongs to the father, then the paternal grandfather, then the executor appointed by the father or the grandfather; otherwise, it falls to the judge. This is the view of the Shafi'i school. However, if by "guardianship" you mean custody, then those entitled to it have already been explained.