It sounds like most of the issues you are having are caused by the fact that your home page is using a Shortcode of VikRentCar rather than the apposite “Search Form” widget. I just visited your website, and it looks like this is exactly the case. The booking form on your home page is not the widget, it is rather the Shortcode of type “Search Form”, and that’s not supposed to be in your home page.
In order for the routing functions and landing pages to work properly during the booking process, the home page, which is a special page of WordPress with an empty “page ID”, should not contain any Shortcode of VikRentCar, which would render a page. In your website home page you are only supposed to publish widgets of VikRentCar. Not sure how you manage your WordPress pages, but any content builder plugin would let you publish the widget “Search Form” of Vik Rent Car in that same exact position where you currently have the Shortcode.