Hooks around add to cart for Woocommerce

I am running a WooCommerce store with WC Marketplace. What I am trying to achieve with the hook below is to prevent a new item being added to a basket if there is already a product in the basket from a different vendor. e.g. If a shopper adds product x from vendor y to his basket, if they were to add product a from vendor b, then the item will not be added and the user will be informed of the error.

I have 2 questions:
- firstly when does a hook run, is it before the main function fired or after? I have a hook for the function woocommerce_add_to_cart. So I want to know will the hook fire after the function woocommerce_add_to_cart runs or before.
- My second question is, I have attached the hook below, in your opinion would this work?

function action_woocommerce_add_to_cart( $cart_item_key, $product_id, $quantity, $variation_id, $variation, $cart_item_data ) { 
    $same_vendor = 1;

    $empty = WC_Cart::is_empty();

    //If there is an item in the cart then,
    if (!$empty) {
        //Get the VendorId of the product being added to the cart.
        $vendor = get_wcmp_product_vendors($product_id);
        $vendor_id = $vendor->id;

        foreach( WC()->cart->get_cart() as $cart_item ) {
            //Get the vendor Id of the item
            $cart_product_id = $cart_item['product_id'];
            $cart_vendor = get_wcmp_product_vendors($product_id);
            $cart_vendor_id = $cart_vendor->id;

            //If two products do not have the same Vendor then set $same_vendor to 0
            if($vendor_id !== $cart_vendor_id) {
                $same_vendor = 0;
            }
        }

        if ($same_vendor === 0) {
            WC()->cart->remove_cart_item( $cart_item_key );
            //How do I show a message to tell the customer.
        }
    }
}

Regards