The answer to this question lies in your code for the second carousel which you didn't provide.. I just made a jsfiddle very quickly from your code. It's not having any good markup so I would recommend to rewrite it. http://jsfiddle.net/PQQEe/
Basically you probably forgot to change some variables appropriately.. like your t.find..
Lets say the 2nd carrousel has the id "more". So your JS would look like:
$(document).ready(function() {
var t = $('#featuredAppartments ul');
$('#featuredAppartments .next').click(function(event) {event.preventDefault();t.find('li:first').appendTo(t);});
$('#featuredAppartments .pre').click(function(event) {event.preventDefault();t.find('li:last').prependTo(t);});
var d = $('#more ul');
$('#more .next').click(function(event) {event.preventDefault();d.find('li:first').appendTo(d);});
$('#more .pre').click(function(event) {event.preventDefault();d.find('li:last').prependTo(d);});
});
You now select the buttons by the carousel ID and you also only access the list within each carousel. Hope it helps.