It’s not clear from your post what type of green card application you’ve already submitted, so it's difficult to give you a precise answer.
In any event, if an I-130 petition, I-140 petition, I-485 application, or DS-230 application has already been submitted, then you should have a receipt notice that you can present to CIEE.
If indeed you have started the green card application, then it could now be difficult to get a J-1 visa. In order to get a J-1 visa, you have to show that you don’t plan to permanently immigrate to the US. Having started the green card application process obviously shows that you do plan to immigrate to the US, and therefore your J-1 application could be denied.
You should speak to the attorney processing your green card application to clarify things.
Attorney Edward Weiner
http://www.immigration-aux-usa.com/