Your Inn Style booking engine is a website. And while it can do lots of clever things, it's still fundamentally a website. So you can – if you choose to wield such sharp technical knives – do lots of custom things.
But if you have customised the way people reach your Inn Style booking engine, you will need to use Linker to ensure Google Analytics works.
This means you'll need to add the following Javascript to your website:
// Loads the Linker plugin
ga('require', 'linker');
// Instructs the Linker plugin to automatically add linker parameters
// to all links and forms pointing to the domain "innstyle.co.uk".
ga('linker:autoLink', ['innstyle.co.uk'], false, true);
The magic here is in the fourth argument of true in the code above.
This instructs the Linker to add a linker parameter to form submissions that point to destinations matching the domain parameter.
If you've done this correctly, when you submit your respective form or click the link that takes your customer to the Inn Style booking engine, you will see a parameter in the URL that looks like this:
_ga=1.199239214.1624002396.1440697407
If you don't see something like this, then Linker is not running correctly. Check your code again thoroughly, and look for errors in your Javascript console.
If it is present and valid, Inn Style will extract the client ID from the parameter and store it against the session so your user journeys can be tracked all the way from acquisition (via Facebook, Google Ads etc) through to booking completion.