Is there a way to combine $(this) with :nth-child?

What you need is context. With context, the selector will only look for elements that are the children of the context (in this case this).

$(':nth-child(2)', this).attr('id');

jsFiddle Demo

This is basically the same as:

$(this).find(':nth-child(2)').attr('id');

If you only need the direct children, not every descendant, you should use .children():

$(this).children(':nth-child(2)').attr('id');