There isn't a direct solution to having both while in the far right side of your page. JFBConnect uses the Like button from Facebook. That button has an option to show the share button as well, but only when rendered using the HTML5 method. The HTML5 method, however, uses the popup that is causing you issues.
When you disable the Share button from the Like button, the JFBCSocialShare module uses the iFrame version of the Like button. The iFrame version doesn't use the popup, which is why it works when that's disabled.
Now that you've set the width down to 50, you may be able to re-enable the Share button. Then, the popup will simply be hidden, but you still may see something when clicked. The only other option I can recommend is moving the JFBCSocial Share to the left side of the screen so that the popup can work going to the right.
There's really not anything more we can do about this, but I hope that gives you some clarity and ideas.
Thanks,
Alex