WooCommerce: update custom fields after checkout validation failure

Question

In my project I'm customizing some of the WooCommerce features.
My "shipping methods" are:
1. delivery
2. take away

I also added a custom field in the checkout page that is a <select> populated with the valid times for delivery (case "1") or for the take away (case "2").

It may happen that a user selects 2. take away in the cart page, then selects a time valid for "2", but then changes to 1. delivery and the selected time may not be valid anymore, neither the option list and the custom field label.

Of course i'm using the woocommerce_checkout_process hook to warn the user via wc_add_notice(), but even if the woocommerce_checkout_fields hook is triggered (that's where i create the select list), the <select> values are not updated.

I think there is an AJAX call that is related only to the shipping method and doesn't update the other checkout fields, although woocommerce_checkout_fields hook is triggered.

How to update the custom fields? Do i need some js/jquery/AJAX?

Or: can a custom field be related to a shipping method (and get updated via AJAX with it)? How?

EDIT

Custom field code:

add_filter( 'woocommerce_checkout_fields', 'fty_filter_checkout_fields' );
function my_filter_checkout_fields($fields) {
    $must_deliver   =   WC()->cart->shipping_total > 0.0;   // true=deliver, false=take away

    // some complex code to calculate time lists omitted, samples array instead:

    $delivery_time_list =   array(
        "deliver 10:00",
        "deliver 11:00",
        "deliver 12:00",
        "deliver 13:00"
    );

    $takeaway_time_list =   array(
        "takeaway 10:00",
        "takeaway 10:30",
        "takeaway 11:00",
        "takeaway 11:30",
        "takeaway 12:00",
        "takeaway 12:30",
        "takeaway 13:00",
        "takeaway 13:30"
    );

    // add the new conditional field
    if($must_deliver) {
        $fields['my_delivery_datetime'] = array(
            'my_delivery_time' => array(
                'type'      => 'select',
                'options'   => $delivery_time_list,
                'required'  => true,
                'label'     => __('Delivery time')
            )
        );
    } else {
        $fields['my_delivery_time'] = array(
            'my_delivery_time' => array(
                'type'      => 'select',
                'options'   => $takeaway_time_list,
                'required'  => true,
                'label'     => __('Take away time')
            )
        );
    }

    return $fields;
}

an idea of the validation code:

add_action('woocommerce_checkout_process', 'my_checkout_date_time_validation', 30, 1);
function my_checkout_date_time_validation($doh) {
    $time = filter_input(INPUT_POST, 'my_delivery_time');
    $shipping = filter_input(INPUT_POST, 'shipping_method', FILTER_DEFAULT, FILTER_REQUIRE_ARRAY);

    if(strpos($time, "deliver")!==FALSE && strpos($shipping[0], "local_pickup")!==FALSE) {
        wc_add_notice('Please re-select take away time', 'error');
    } else if(strpos($time, "takeaway")!==FALSE && strpos($shipping[0], "distance_based_rate")!==FALSE) {
        wc_add_notice('Please re-select delivery time', 'error');
    }

}

here's about shipping methods;

add_action( 'woocommerce_flat_rate_shipping_add_rate', 'add_distance_based_delivery_rate', 10, 2 );
function add_distance_based_delivery_rate( $method, $rate ) {
    $new_rate          = $rate;
    $new_rate['id']    .= ':' . 'distance_based_rate';
    $new_rate['label'] = 'delivery'; // Rename to 'Rushed Shipping'.

    // incredibly complex code used to calculate delivery costs omitted
    $dist_cost  =   1000;

    $new_rate['cost']  += $dist_cost;
    $method->add_rate( $new_rate );
}

Thanx!