Code should not mix pointer types. On systems where sizeof(unsigned short) < sizeof(int), this is a program flaw.

 // int *children = malloc(size * sizeof(unsigned short));
 int *children = malloc(size * sizeof(int));
 // or even better
 int *children = malloc(size * sizeof *children);

For high portability, use type size_t or unsigned long for values that may exceed 65,535:

 // unsigned int size = count_children(input);
 size_t size = count_children(input);
 int *children = malloc(size * sizeof *children);

Code should check the return value from fscanf(input, "%d",&count); and fscanf(input, "%d",&children[i]);

Mixing types for finding the maximum is very questionable. Suggest re-write

size_t chck_tall(const int *children, size_t size) {
  size_t total = 0;
  int tmp_max = 0;   // or maybe INT_MIN
  for(size_t i = size - 1; i-- > 0; )  {
    if(children[i] > tmp_max) {
      tmp_max = children[i];
      total++;
    }
  }
  return total;
}

Code should not mix pointer types. On systems where sizeof(unsigned short) < sizeof(int), this is a program flaw.

 // int *children = malloc(size * sizeof(unsigned short));
 int *children = malloc(size * sizeof(int));
 // or even better
 int *children = malloc(size * sizeof *children);

For high portability, use type size_t or unsigned long for an array index that may exceed 65,535:

 // unsigned int size = count_children(input);
 size_t size = count_children(input);
 int *children = malloc(size * sizeof *children);

Code should check the return value from fscanf(input, "%d",&count); and fscanf(input, "%d",&children[i]);

Mixing types for finding the maximum is very questionable. Suggest re-write

size_t chck_tall(const int *children, size_t size) {
  size_t total = 0;
  int tmp_max = 0;   // or maybe INT_MIN
  for(size_t i = size - 1; i-- > 0; )  {
    if(children[i] > tmp_max) {
      tmp_max = children[i];
      total++;
    }
  }
  return total;
}