Q:

Can't find children of element

for some reason i'm unable to get the children from the div with the classname of .slideshow-dots.  Here is the div with it's children:
<div class="slideshow-dots">
<span class="dot"></span>
<span class="dot"></span>
<span class="dot"></span>
<span class="dot"></span>
</div>

And this is the error:

Uncaught TypeError: Cannot read property 'className' of undefined

Below is my code, i'm also unable to call the public method showSlides. 
(function($) {
    $.fn. MarvSimpleGallery = function( options ) {
      var instance = this;
      instance.index = 1;

      var settings = $.extend({
        // These are the defaults. 
        arrows: true,
        dots: true,
        numbers: true
      }, options );

      var init = function() {
        instance.dotCont = instance.find('.slideshow-dots')[0];
        instance.slides = instance.find('.mySlides');

        // Assign event listeners
        instance.find('.prev').click(function() { instance.showSlides(instance.index += -1); });
        instance.find('.next').click(function() { instance.showSlides(instance.index += 1); });

        // Initiate dot controls
        $.each(instance.slides, function(index, data) {
          var dot = $('<span></span>');
          dot.addClass('dot');
          dot.click(function() { instance.showSlides(instance.index = (index + 1)); });

          $(instance.dotCont).append(dot); 
        });

        // Show initial slide

      }();

      instance.showSlides = function(n) {
        console.log('Slide: ' + n);
        if (n > (instance.slides).length) instance.index = 1;
        if (n < 1) instance.index = (instance.slides).length;

        var slideCount = (instance.slides).length;

        $.each(instance.slides, function(index, data) {
          data.style.display = "none";
          $(data).prepend($('<div></div>').addClass('numbertext').append((index + 1) + ' / ' + slideCount));
        });

        instance.slides[instance.index-1].style.display = "block"; 
        $(instance.dotCont).find('dots')[instance.index-1].className += " active";
      };

    }
  }(jQuery));

A:

try
$(instance.dotCont).find('dot')[instance.index-1].className += " active";

instead of 
$(instance.dotCont).find('dots')[instance.index-1].className += " active";

Your children elements have the class 'dot' and not 'dots'. 
Edit - as said in comment:
i forgot the dot:
the final sentence must be 
$(instance.dotCont).find('.dot')[instance.index-1].className += " active";

