That's clearer. If the booking engine has it's own form, and you want to embed it in a page that you can style to look part if your site, then an IFrame is the way to do it. Whether you embed it in an existing page or one set up specifically for it is up to you.
As an alternative, it my be possible to take the form input in your own form and pass the results to the engine, but that:
a) Is more work.
b) May need to be written in PHP.
c) Requires a depth of understanding of the data input.
d) Is liable to be broken if/when the input structure of the target form changes.
It's much easier, and more robust, to just link the engine's own input page in an IFrame. However, I've done my own input form on my site to front-end the W3C HTML5, CSS3 and links validators, but there the input is fairly simple. I added my own input form so I can pass the input to the three validators simultaneously, all embedded in IFrames in the same page. If you want to see how that works go to http://www.emberwebsites.co.uk/ and select the HTML5 Validation Suite.