I'm not sure with UVerse, but maybe after reading this, you can figure it out. With a cable box or satellite box, if you are watching the signal from your cable box or satelllite box, you have to watch the same channel that is being sent to your tv. You can run an additional coax cable directly from the wall to your Slingbox Pro-HD and that allows you to watch a different channel on your Slingbox. This signal will not come from your cable box or satellite box, so you cannot watch premium channels or scrambled channels, etc. Now with UVerse, you may be able to do the same thing, someway, but I'm not sure. I suppose someone who knows for sure will weigh in here or you can do a search.
The simple answer is just to identify the TV source. If the Slingbox and the TV are getting their signal from the same source then changing on the laptop will change the TV. If they are getting the signal from different sources then it won't happen.
So if you are using cable then get a second cable box, if you are using satellite, get a second box.
Remember, the Slingbox is just another TV that happens to send it's signal down the Internet rather than to a screen. So it needs the same extra equipment you would need if you bought another TV.