It is possible to do it. But that's a conditional "yes." It depends a lot on how you get your TV service and a little on how you have things hooked to the Slingbox.
If you're both watching the same video source, you're stuck- you're both going to see (and remote control) the same thing. That's what you've got now.
But remember, the Pro HD has three independent inputs. The source shared with your TV at home uses one. That's fine, leave it that way.
You need to connect a separate source up to one of the other Slingbox inputs. When you do, you can flip over to that and watch it without disturbing the home TV.
Ideally, you subscribe to cable TV service that includes analog expanded basic channels on all coax outlets. Even if you have digital cable, some providers include this service automatically as part of the package. If so, just hook a cable coax from the wall up to the tuner and you're all set.
If you don't get that service or use Satellite TV, you'll need to order a second box to pull this off. Slingbox can handle two cable/sat boxes at the same time: one on its HD component input and one on its SD composite input.
One final option is to attach an antenna up to the Slingbox tuner input. If you're in range of your local broadcast TV stations, you can pull their signals out of the air for free and watch that. It may not be ideal, but it is a separate source.
Hope this helps !