wordpress plugin noob situation

Rather than include an HTML file, include a PHP file instead. Then, at the top of your PHP file you can check to see if any data’s been submitted and process it before displaying the form. So instead of what you have, try:

function show_hotel_dashboard(){
    include 'dashboard.php';
}

Then on the page do things like:

<a href="https://wordpress.stackexchange.com/questions/1210/dashboard.php?action=do_something">Do something</a>

And in your dashboard.php file, start with

<?php
if($_POST["action"] == "do_something") {

    // Do something

} else {

    // Output your regular dashboard page

} ?>