Happy to answer my own question. Here's what you do to reload the panel, by creating a simple button that reloads the 'window'. Useful for Illustrator scripts.
In yout HTML:
<button id="bt_reload" class="hostButton">Reload</button>
In your main.js file (or similar)
$("#btn_reload").click(reloadPanel);
// Reloads extension panel
function reloadPanel() {
location.reload();
}