Hi Paul,
I am an English web developer but living and working in Pattaya over on the darkside - see regular updates on facebook about PattayaCentral.
Your current site is built on wordpress which is a solid platform and best option available for managing a website currently.
However for specialist functionality (eg. bookings) it is limited to whats in existing plugins, or build your own plugin.
This gives us a couple of choices to proceed:
1)Keep wordpress with the existing booking plugins and modify them to work better
2)Keep wordpress & build a new plugin(s) to manage your bookings in the way that works best for you
3)Content on wordpress but move the bookings to an external custom built booking platform (I have a strong starting point already)
4)Build a custom booking system and website from scratch
All are viable but 1-3 would be the most effective - it would take a lot of work to make a content management system that gets close to the flexibility & ease of use that wordpress provides.
Your current site is looking nice, plus is responsive so I would need more information on what you view as its downsides and why you are looking to replace it in order to offer the best solutions.
The booking process seems to work ok but some parts could flow easier or make suggestions as typing. Upsells or suggested extras would help.
SEO is a long term and complex process so best to approach that separately, but any work would be done with SEO in mind (but that alone isn't enough!)