Yes, and yes, what you're describing isn't complicated and should be fine.
Note that the Mini will be your only possible issue since it can only pull Live TV off of its host DVR, but it can easily do recorded content from both, so some live channels will be sub-optimum on the mini.
Note that the Mini will be your only possible issue since it can only pull Live TV off of its host DVR, but it can easily do recorded content from both, so some live channels will be sub-optimum on the mini.