If you have a living grandparent you should for sure have him tested. Autosomal DNA only goes back so many generations, and by testing him you get a two generation jump further back. Plus, your DNA has been "diluted" twice since him so you only have about 1/4 of his. Adding this with all the other lines really confuses the picture.
Now, I will tell you if he or both his parents are actually from Italy, you will get way fever cousin matches because most of the people testing are in the U.S.