olJim,
Greetings, nice to see you online again, hope you and yours are well.
AlaskanPrincess,
I'm not all that familiar with the 222K unit, but I will agree with Jim, on the Terk equipment !
Customarily, when one combines OTA (the Antenna) with a Dish, it's done via two or more Diplexers.
Those are little gadgets which first, you input both the Antenna and Dish into one, it combines the signal and sends it on to other Diplexers, one for each Room/TV, and you separate the signals from the (in Room) Diplexer to your Antenna Input and Sat Box there.
Given what I've read in your post, I'd go along with stardust3's advice and get a Pro involved. Preferably one who can also advise you on a GOOD antenna to use, but, there's more information you need, to be assured of what to expect, concerning your OTA.
Your specific location, and what channels are available there, may preclude the need for all this. Right now, you don't know if what you can receive is worth all the trouble. It's something I'd sure want to know, and here's the way to find that out.
Go to this link, where you will find the...
LookUp & Posting Instructions for finding your Free Local TV Channels.
When you've done that (posted your Chart link) I or another qualified person here can comment on the "worth it" and an appropriate Antenna, if it goes that way.
Have a good Day !

S.W.