So you're thinking of getting a Genie DVR setup for your main home? If so, and you keep your dish at the summer cabin, then yes you can take the Genie DVR to your summer cabin and watch its recordings. But you'll also need to upgrade your summer cabin dish to a "Single Wire Multiswitch" (SWM) dish because the Genie won't work with your standard Receiver's dish (unless it happens to be SWM already), and you need an active satellite connection for the DVR to continue functioning.
You could also record the Genie DVR shows to VHS or DVD Recorder. You would need to record them in "real time" while playing them on the Genie DVR because there's no way to transfer them digitally.
If you have a fast internet connection at the summer cabin, you could consider getting a "GenieGo" box so that you could stream your Genie DVR's recordings to your summer cabin via a laptop, iPad, etc. You could connect the iPad to your TV if you want.