I don't see a problem simply splitting the inputs. With the audio, it would only be a problem if you were sharing the speakers (putting an extra load on them). But keeping the same amp, and just splitting the input is fine.
As for the video, I don't think there is a problem either. But to be on the safe side, I'd check the ground lines from both systems to make sure they have the same "ground potential" (relative to a common earth ground, or to the other inputs from each system). If there is a problem or you wanted to play it safe, you could use diodes.