move request a quote button - add this code in the file functions.php of your theme

scratch_1.php

<?php 

/* To move request a quote button in the loop */
if( class_exists('YITH_Request_Quote_Premium')){
  remove_action( 'woocommerce_after_shop_loop_item', array( YITH_Request_Quote_Premium(), 'add_button_shop' ), 15 );
  add_action( 'your_loop_hook', array( YITH_Request_Quote_Premium(), 'add_button_shop' ) );
}

/* To move request a quote button in the single page */
if( class_exists('YITH_YWRAQ_Frontend') ){
  remove_action( 'woocommerce_single_product_summary', array( YITH_YWRAQ_Frontend(), 'add_button_single_page' ), 35 );
  
  //to move button near the add to cart button
  add_action( 'woocommerce_after_add_to_cart_button', array( YITH_YWRAQ_Frontend(), 'add_button_single_page' ) );
}