Changing shipping method doesn't update total cart price in checkout page

Question

I have separated the cart recap (review-order) from the rest of the checkout page.

.woocommerce-checkout .shop_table.woocommerce-checkout-review-order-table
    {
        display: block !important;
        position: absolute;
        top: 0;
        left: 0;
        float: none;
        width: 455px !important;
        background-color: #f6f6f6;
    }

It's on the left now. I am also using the plugin ̀ YITH WooCommerce Multi-step Checkout Premium` to split the checkout in several steps.

The issue is that when the user changes the shipping method the total price is not updated. As you can see in the attached image, total price should be 100,90 EUR.

In WooCommerce > status, I don't any warning on templates, except form-checkout.php because I've updated the file the Yith plugin is hacking.

Edit

I have this js in child theme :

if ( jQuery('body').hasClass('woocommerce-checkout') ) {
    jQuery(".woocommerce-checkout-review-order-table").prependTo(".woocommerce");
}

in order to keep .woocommerce-checkout-review-order-table always visible, because the plugin I am using YITH WooCommerce multi-step checkout hides the whole #order_info at certain steps, and to position it like this:

.woocommerce-checkout .shop_table.woocommerce-checkout-review-order-table
{
    display: block !important;
    position: absolute !important;
    top: 0;
    left: 0;
    float: none;
    width: 455px !important;
    background-color: #f6f6f6;
}
.woocommerce-checkout h3#order_review_heading {
    display: none;
}
.woocommerce-checkout .woocommerce-checkout-review-order-table thead {
    display: none;
}

Nathalienathan

sorry, I added info. Actually maybe it's the plugin from Yith that is blocking the ajax update... – Nathalienathan

As you are using YITH WooCommerce Multi-step Checkout Premium plugin, it's not possible to help you on that, as this is something much more complicated that can't be handled on StackOverFlow. What happens is that your actual review-order is not anymore refreshed on "update_checkout" Ajax event. – Turaco

Exactly, that's what happens. I've contacted the support of the pluging to get help on this. Thanks for your message @Turaco – Nathalienathan

@Turaco actually it's not the plugin that causes the issue. I deactivate the plugin and removed the corresponding custom files in the child theme dir. And the bug is there. Can you go and check it here if you find something : staging.hemen-biarritz.com/checkout ? – Nathalienathan

the problem is that you can't separate things as you are doing… – Turaco