Sorting Each Entry (code review + optimization)
There are many improvements that can be done, but here are a few things I identified:


I wouldn't have the require call within the function itself. I would rather create a top-level module with all listed dependencies. The updateBottomBar function would be defined in this module:




require(["dojox/collections/ArrayList"/*, other deps...*/], function(ArrayList) {
    function updateBottomBar() {
        //...
    }
});


Have a look at https://dojotoolkit.org/documentation/tutorials/1.8/modules/


It's very inefficient to merge the multiple arrays every-time. You should rather maintain an additional array that stays in sync with the others. When a new item is pushed in one of the other arrays, you reflect the changes in that additional array directly (same logic with removal). However, if you can, I would rather have a single collection to maintain and use a discriminator such as a category property to categorize items, so instead of holding strings, the collection would contain { country: String, category: String } objects.
With your current implementation, you also throw away some useful information that you need to recompute later. For example if(selectedCountries.contains(country)) shouldn't be necessary since you had that knowledge when you pushed the items in the bottomBar list. Instead of pushing a simple string, push an object like proposed in point #2. Then you will be able to check if the items belongs to the selected category in O(1) time by doing something like:

switch (country.category) {
    'selected': //do something break;
}

Concatenating multiple strings with the + operator isin't the most efficient way. Instead you should push your strings in an array and then use theArray.join('') to perform the concatenation. 

Also note that you can create DOM elements dynamically with document.createElement and make the process efficient by using document fragments (document.createDocumentFragment).
You have a typo -> var initalContent="Countires: &lt;label&gt;";
initalContent != ... Did you mean += ?