I don’t know how your CSS is build, but I woud suggest a rather simple Javascript code that detects the screen resolution and acts consequently.
<SCRIPT language="JavaScript">
<!--
if ((screen.width>=1024) && (screen.height>=768))
{
//set your sidebar DIV display to "none";
}
else
{
//set your sidebar DIV display to "block";
}
//-->
</SCRIPT>
I don’t know if that can help you, but I think it can be a simple solution!