I think the answer depends on how your dad's TV is configured. For example, I have a TV at my vacation home in one state that has four "signal input" connections on it -- one for RF signal input, one for composite (Red-White-Yellow cable) input on the back of the TV, one for component (3 video cables plus 2 audio cables) on the back of the TV, and one for composite (Red-White-Yellow cable) input on the front of the TV. The first one connects the incoming TV signal from the wall directly to the TV display. The second connects my DVD player to the TV display, the third connects my Tivo to the TV, the fourth connects my VCR to the TV display.
I have the Slingbox connected to the Tivo. Since the Tivo receives all of the incoming TV channels, I can watch on my main home computer (or on my laptop anywhere in Internet land) any of the channels that the vacation TV would receive, while at the same time, a person in the vacation home can watch any of the channels coming through the direct TV signal connection to the TV. They can also watch any of the DVDs, or any of the VCR tapes, while I am merrily watching TV through the Tivo connection. BUT, if they cycle their remote to the input signal that connects the Tivo to the TV, then they will see whatever I happen to be watching at the moment through the Slingbox connection. And if either of us changes the channel that the Tivo is broadcasting, both of us will see the changes.
So, to make a long story short, you can watch your dad's channels on your Slingbox without disturbing his viewing IF he has at least two separate connections on his TV supplying the broadcast signal to the TV. If he doesn't have a Tivo, it could be two cable boxes, or a cable box and a "digital transport adapter" -- think of this as a no-frills cable box, Several television service providers now will provide a couple of these DTAs to each customer for free, as part of their conversion-to-all-digital transition. In my case, my local service provider Comcast provides one cable box and two DTAs for free, and additional DTAs can be rented (but not purchased) for $2 per month extra each.