I use .append to add to a div
$(this).append('<ul><li>test</li></ul>');
how can I search for a <ul> and remove it if it exists in the children of $(this)?
You could use remove(). More information on jQuery remove().
$(this).children("ul").remove();
Note that this will remove all ul elements that are children.
The opposite of .append() is .prepend().
From the jQuery documentation for prepend…
The .prepend() method inserts the specified content as the first child of each element in the jQuery collection (To insert it as the last child, use .append()).
I realize this doesn’t answer the OP’s specific case. But it does answer the question heading. :) And it’s the first hit on Google for “jquery opposite append”.