All of my mornay sauces comes out a tad bit grainy, is it better to just use heavy cream and then add cheese

Not sure if you used freshly shredded cheese done at home, or the pre-shredded product from stores, but... I prefer shredding my own blocks of cheese to avoid the fillers often used for keeping shredded cheese from clumping. POLC brings up some great points about the in-the-making process...

OOOPH save the heavy cream for alfredo/cream sauce... :)

The way I make a mornay sauce is by making a béchamel and then adding a cheese that will melt without splitting or seizing (I find some good quality cheddars and parmesans end up being an oil slick). It's important that you don't let your béchamel boil, and you add the cheese off the heat and in increments. I usually pull the sauce, give it a stir for a minute or so, then add the cheese. I never use heavy cream, though...milk is plenty rich.