You could certainly use WordPress, there are several reservation system plugins. A quick search and I found Restaurant Reservations -- which would cover the whole table management part. It has add-ons including customizing forms. And it's developed in GitHub.
If you were looking for something more in the customer management area you could check out this list of CRM plugins. I did take a quick look at WP-CRM and one positive review was from someone managing a club website.
If you wanted to incorporate a CRM application and get some advanced customer management features, check out this link on CRM types. Several CRM's offer WordPress plugins or ways to easily link to them from a web site.
Looking at it the other way, you have few users and some unique needs that merge customer management and booking systems. If you have experience with CSS and forms you could certainly add some custom pages with the exact features you want. You would have to include a database to store member, event and reservation data. Personally, I see this as the high maintenance option.
WordPress offers so much flexibility today that I would check out the plugins first.