The problem that the price for the cart widget and checkout page is taken from one place in WooCommerce code. You find it in the file woocommerce/includes/class-wc-cart.php
public function get_product_price( $product ) {
if ( 'excl' === $this->tax_display_cart ) {
$product_price = wc_get_price_excluding_tax( $product );
} else {
$product_price = wc_get_price_including_tax( $product );
}
return apply_filters( 'woocommerce_cart_product_price', wc_price( $product_price ), $product );
}
Regards