Wouldn't the coaxial cable from the dish go to your receiver, and then you would have an HDMI cable from the receiver output to an input on your HDMI splitter? I assume that all 3 of your TV's have an HDMI cable going into the output jacks on your splitter - that's how mine was set up. I am assuming, of course, that your HDMI splitter has at least 3 output jacks.
I ultimately went with 2 receivers so that I could watch different programs on different TV's.