Is there a way to tell the server or client-side script on my website that your modals are visible or not?

Yes, there is. Please run the following JavaScript in your Parent page:

There is a JavaScript event that you can subscribe and you will be notified when one of the campaigns is popping up.

$('html').on('optimonk#campaign-show', function(event) {
console.log('event: ', event);
console.log('event.parameters: ', event.parameters);
});