I'm guessing that you have, but on the CATV input that has the splitter, have you tried both of the outputs?
From everything that I've read and heard, Directv signals are higher frequency than cable and antenna signals. The Directv-approved splitters that I've seen generally go up to the low 2GHz in frequency. The H15 specs list those coax inputs/outputs as 5MHz to 1GHz. My guess is that is sufficient for pass-through (as it's working fine on the set that isn't split) but isn't a high enough frequency to work when the line is split. If the splitter has one line that is a power pass (which I'm still a bit unclear on), that line might might work better than the other.