That’s really a good practice of making back-up of your site. As you had done custom changes on your child theme, you needn’t have to delete the child theme. Just delete the parent theme and update to latest version.
let us know if you got any problems on this , we will be more than glad to assist you
We will surely present that tutorial on more details. Could you tell us where you are confused most, so we can make changes accordingly.
And about child theme, it’s different theme which inherits just the template of parent theme. So for example if you had done custom changes on your header.php file and when you updated your parent theme to latest version ,WordPress will take header.php template of child theme instead of parent header.php.
So there will not any problems on updating parent theme, if you didn’t have made any changes on core template.
Hope this clarifies your queries , if not please feel free to ask a question, we will be more than glad to assist you.