Step 1
obj = dt << Variability Chart();
will open the Variability Chart dialog box, and when the user clicks on OK, all of the charts will be run at that time.
However, once the Variability Chart has been run, you can query the script returned from the Variability Chart Platform and get the X's and Y's
obj = Variability Chart( Y( :NPN1, :PNP1 ), Model( "Main Effect" ), X( :SITE ) );
theScript = char(obj << get script);
theYsList = words(word(1,substr(theScript,contains(theScript,"Y(")+2),")"),",");
theXsList = words(word(1,substr(theScript,contains(theScript,"X(")+2),")"),",");
For step 2, you can query the Displayed Plot directly and get the various settings. Take a look in the Scripting Index for how to get the framesize, min and max and increment for the various axes etc, that you will need to apply to the additional applications of the Variability Chart.
I think that your suggested approach is going to be more trouble than benefit. I suggest that rather than using the Variability Chart dialog box, but you rather create your own dialog box, resembling the Variability Chart dialog box, which will then set you get all of the information you need up front, and then steps 2 and 3 will become much easier to implement.
See the Scripting Guide for information on how to create your own new window.dialog box
Jim