magento2 – Magento 2 how to update cart price is modified?

I have a form, and when I submit the first time it adds a product with a custom price, that works fine, then I go to the checkout without problem, but when i hit the back button on browser and change values on the form, the price will change, then if I go to checkout again, new price won’t be shown.

The right total amount will show just after adding billing address information, because it seems like the whole quote-cart component is updated.

This is my code:


 public function execute(){
        $quote = $this->checkoutSession->getQuote();

        $allItems = $quote->getAllVisibleItems();
        $itemsQty = $quote->getItemsQty();

        $request = $this->getRequest()->getPostValue();

        $product_id = $request('product_id');
        $price = $request('grand_total');
        $uniqueid = $request('uniqueid');


            $params = array(
                'formKey' => $this->formKey,
                'product_id' => $product_id,
                'qty' => 0

        $productFactory = $this->product->create();
                //here I clear the cart so the product is not added more than 1
                $product = $productFactory->load($product_id);
        catch(Exception $e){
            return $request;

My submit part on the knockout.js component

                        url: cart_url ,
                        data: {product_id: 1,grand_total:data(0).grand_total, uniqueid: data(0).uniqueId},
                        method: "POST"
                        var sections = ('cart');
                        customerData.reload(sections, true);
                         window.location.href = checkout_url;
                    }).fail(function(jqXHR, textStatus){

When I’m redirected to checkout the new price is not shown, just the old one, until I add billing information and hit update it shows the new price.

What am I doing wrong?