Click event not always fireing in Drupal behaviors
See comments below...    

      .on('submit', function(e){ // Not correct way of using submit.
                e.preventDefault();
                var $form = $(this); // You have already defined this global variable?

                $(function () { // you dont need to check if the document is ready, thats what behaviours are for.
                    $('#mymodule-form').submit(function () { // Why are you submitting again here?
                        if($(this).valid()) {
                            $submitButton.trigger('submitmyform'); // What are you trying to trigger?
// If the form is already submit, why are you doing anything with the submit button?
                        }
                    });
                });

            });


Try this...

var $form = $("#mymodule-form", context);

$form.submit(function(e){
  e.preventDefault();
    if($(this).valid()) {
       // Do something else...
    }
});


UPDATE

You are probably binding to the form before it exists. Bind the event to the document, and pass the form selector...

$(document).on('submit', '#mymodule-form', function(e){
    // Do something...
});