How to trigger an event after using event.preventDefault()

Nope. Once the event has been canceled, it is canceled.

You can re-fire the event later on though, using a flag to determine whether your custom code has already run or not – such as this (please ignore the blatant namespace pollution):

var lots_of_stuff_already_done = false;

$('.button').on('click', function(e) {
    if (lots_of_stuff_already_done) {
        lots_of_stuff_already_done = false; // reset flag
        return; // let the event bubble away
    }

    e.preventDefault();

    // do lots of stuff

    lots_of_stuff_already_done = true; // set flag
    $(this).trigger('click');
});

A more generalized variant (with the added benefit of avoiding the global namespace pollution) could be:

function onWithPrecondition(callback) {
    var isDone = false;

    return function(e) {
        if (isDone === true)
        {
            isDone = false;
            return;
        }

        e.preventDefault();

        callback.apply(this, arguments);

        isDone = true;
        $(this).trigger(e.type);
    }
}

Usage:

var someThingsThatNeedToBeDoneFirst = function() { /* ... */ } // do whatever you need
$('.button').on('click', onWithPrecondition(someThingsThatNeedToBeDoneFirst));

Bonus super-minimalistic jQuery plugin with Promise support:

(function( $ ) {
    $.fn.onButFirst = function(eventName,         /* the name of the event to bind to, e.g. 'click' */
                               workToBeDoneFirst, /* callback that must complete before the event is re-fired */
                               workDoneCallback   /* optional callback to execute before the event is left to bubble away */) {
        var isDone = false;

        this.on(eventName, function(e) {
            if (isDone === true) {
                isDone = false;
                workDoneCallback && workDoneCallback.apply(this, arguments);
                return;
            }

            e.preventDefault();

            // capture target to re-fire event at
            var $target = $(this);

            // set up callback for when workToBeDoneFirst has completed
            var successfullyCompleted = function() {
                isDone = true;
                $target.trigger(e.type);
            };

            // execute workToBeDoneFirst callback
            var workResult = workToBeDoneFirst.apply(this, arguments);

            // check if workToBeDoneFirst returned a promise
            if (workResult && $.isFunction(workResult.then))
            {
                workResult.then(successfullyCompleted);
            }
            else
            {
                successfullyCompleted();
            }
        });

        return this;
    };
}(jQuery));

Usage:

$('.button').onButFirst('click',
    function(){
        console.log('doing lots of work!');
    },
    function(){
        console.log('done lots of work!');
    });