Ok. JM42 is right.
A pre-amp (on the antenna) helps with weak signals.
A distribution amp helps split an incoming signal and distribute it to several receivers.
If there are only two receivers, a splitter will most likely be all you need.
If you can currently receive OTA just fine, as you indicate, you don't need a pre-amp either. But an outdoor antenna may be better.
I have done what you describe. It works just fine.
If you want both TVs to have OTA, take the coax from the OTA antenna into a splitter. Take one of the splitter's outputs, and one of the coax from the dish, to the diplexer. One coax comes out of the diplexer to near the receiver, where the other diplexer will be. That coax goes in, two come out; one to the sat input (they're marked) and the other to the TV Ant input (or directly to the TV if you prefer). Do the same for the other receiver, from the other output from the splitter.
Cheap and easy and it works.
Now for the bad news. This won't work with the Hopper/Joey system, which is a whole different creature. Picture your current system as a pony, and the H/J as a unicorn. You feed one hay, the other, magic.