Submitting custom post from frontend,jQuery ajax, and custom validation – can’t find proper place to insert wp_insert_post()

You can achieve the goal through many ways. though the way you have selected is not an appropriate one but you can go with it also. just include the file wp-blog-header.php file (placed at the wordpress root) into validation.php above all other code. you can find all the wordpress related functions will work like a charm.