Help with integrating Internet Cable and Directtv

Mom's house got two cable lines going into the house. And, with her Directv, both of these cable lines are used in order to feed a receiver in the living room and another in the master bedroom.

Now, my mom wants to get Internet Cable. The cable guy showed up this morning and claimed he couldn't install the Internet Cable because both of the two cable lines are already being used by the Directv dish. So, I went to RadioShack and bought a digital quality COAX splitter and tried to split one of the lines from the dish to feed both receivers, but only one receiver will get signal at a time.

Is there anything else I can do? Is there a way to split a directv line? If all else fails, I can call Directv to have them haul their butts here to reinstall the dish. The cable guy claimed the dish guy should have only used one line but is easier to use both lines so... But, I hope I can do this myself. So any ideas will be appreciated.

Thanks.