To answer your question, I believe you COULD aim your (I assume) 18 inch DirecTV dish to say, 119 and have your Dish Network receivers recognize it. The main problem with this is that you are going to be missing a lot of channels that come from 110 with this setup if you subscribe to anything greater than AT60.
Now, the better thing to do (and it will be done anyway with professional installtion) is to have a Dish500 (or whatever the appropriate dish for your area is) installed so you will be able to pick up all of the necessary satellites (110, 119) and any additional satellites to receive say, your local channels, depending where you live. Also, DirecTV dishes aren't going to work with the DishPro switches and whatnot (at least I don't think they will.. I subscribe to DirecTV myself).
Hope that helps
-Dan