It's probably pausing due to buffering, meaning the BlackBerry connection speed is not as fast as the video speed. Or imagine a trying to drink a thick milkshake through a tiny straw...
I don't think there is a fix for that unless you can get a lower resolution video stream. I don't know about connecting your dvr to the broadband -- doesn't seem likely to me that it would work. The other consideration is streaming video/movies uses a LOT of data. If you are on the 5 Gb data plan, you could go through that very quickly.
Definitely an issue with buffering. You actually will see "Buffering" at the bottom of the videos screen when this is happening. I allow the video to play so that it gets through the aggravating parts of the start and stop and then I start the video from the beginning. Usually because the video has completed the buffer process I can watch the video w/o interruption.
With the DVR you would need a dedicated POTS line in order to connect and order movies, etc. through your satellite service provider.