Italian, since the old man is fluent and Great Grandmama was Calabrian.
I do find my Spanish takes on a very slight Italian accent if I'm not careful. I've learned to temper it by affecting with a "ceceo" [aka all lisp, all the time] and using vosotros.
I don't think using Iberian Spanish is going to make you sound less Italian...
I don't know any Italian dialects with that specific lisp. The lisp gets me into it better, unless there's an off chance of an Icelander in the area...but they're far too breathy to get confusing.