Связанный список, отсортированный программой C

Эта программа должна создавать отсортированный список и сортировать каждого пользователя по имени и фамилии. Я не могу понять, как правильно сортировать имена.

У меня проблема только с функцией append_to_list, остальные функции работают нормально.

Когда я впервые начинаю вводить имена:

user ID:    Last Name:    First Name:
3                Alex          Alex
2                Jones         Alex
1                andrew        john

это нормально, пока я не ввожу имя, которое должно сортироваться между двумя именами, когда я ввожу имя Эндрю, Алекс, это происходит.

 user ID:    Last Name:    First Name:
 4                Andrew        Alex
 3                Alex          Alex
 2                Jones         Alex
 1                andrew        john

но Эндрю, Алекс должен быть между пользователем 2 и 3

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "user.h"
#include "readline.h"

// function append_to_list takes user input from user, id, name and puts it     to the end of the list
// as well as sorts each name alphabetically
struct user *append_to_list(struct user *family)
{
    struct user *cur, *prev, *new_node;

    // generate memory
    new_node = malloc(sizeof(struct user));

    if (new_node == NULL) { 
        printf("malloc failed in append\n");
        return family;
    }

    printf("Enter user ID: \n");
    scanf("%d", &new_node->number);
    printf("Enter user last name: \n");
    read_line(new_node->last_name,NAME_LEN);
    printf("Enter user first name: \n");
    read_line(new_node->first_name,NAME_LEN);

    for( cur=family; cur != NULL; cur = cur->next) {
        if (new_node->number == cur->number) {
                printf("user already exists: %s, %s\n",new_node->first_name,     new_node->last_name);
                free(new_node);
                return family;
        }   
    }       
    for (cur=family, prev = NULL; cur != NULL 
        && (strcmp(new_node->first_name,cur->first_name) < 0) 
        && (strcmp(new_node->last_name,cur->last_name) < 0); 
            prev = cur, cur = cur->next) { 

        if((strcmp(new_node->last_name,cur->last_name) < 0)) break;

        if((strcmp(new_node->first_name,cur->first_name) == 0)) 

        if((strcmp(new_node->first_name,cur->first_name) < 0)) break;
        ;
        }
        // use strcmp == 0 to see if name already exists
        if (cur != NULL && (strcmp(new_node->first_name,cur->first_name) == 0)
            && (strcmp(new_node->last_name,cur->last_name)) == 0) 
        {
                printf("user already exists: %s, %s\n",new_node->first_name, new_node->last_name);
                free(new_node);
                return family;
        }

    // append the linkedlist to the end
    new_node->next = cur;
    // check to see if the node is empty
    if (prev == NULL) {
        return new_node;
    } else  {
        prev->next = new_node->next;
        return family;
    }
}
// function delete_from_list removes a user from the family
struct user* delete_from_list(struct user *family) 
{
    struct user *prev, *cur;
    int id;
    int not_found = 0;
    printf("Enter user ID: \n");
    scanf("%d", &id);

    for (cur = family, prev = NULL; cur != NULL; prev = cur, cur = cur->next) {
        if (id == cur->number) {
                // if only one user on family
            if (prev == NULL) {
                family = cur->next;
            // if user is in the middle of family
            // connects prev node to cur node
            } else {
                prev->next = cur->next;
            }
            printf("user deleted: %s ,%s\n",cur->first_name, cur->last_name);
            free(cur);
        }
        else 
            not_found = 1;
    }
    if (not_found == 1) {
        printf("user not found\n");
    }
    return family;
}   
// function find_user searches the family by ID and matches it with the users name
void find_user(struct user *family)
{
    struct user *p = family;
    int id;
    int count = 0;
printf("Enter user ID: \n");
scanf("%d", &id);

    // compares the family with the user entered ID
    // if the ID is the same count set to 1
    if (p != NULL) {
        for (p = family; p != NULL; p = p->next) {
            if (id == p->number) {
                count = 1;
                break;
            }
        }
    }
    // if count is 1 we know the function found that specific user
    if ( count == 1) {
        printf("user found: %s, %s\n", p->last_name, p->first_name);
    } else {
        printf("user not found");
    }
}

// function printList prints the entire family
void printList(struct user *family)
{
    struct user *p;
    printf("user ID:\tLast Name:\tFirst Name:\n");
    for (p = family; p != NULL; p = p->next) {
        printf("%d\t\t%s\t\t%s\n", p->number, p->last_name, p->first_name);
    }

}

// function clearList clears the entired linked list
void clearList(struct user *family)
{
    struct user *p;
    while (family != NULL) {
        p = family;
        family = family->next;
        if (p != NULL) {
            free(p);
        }
    }
}