Venice is almost four hours from Rome by train, I would say that rules it out. It's a city that (as you can see above, evokes different reactions). My wife had been in Venice before and hated it. It was smelly, overbearing, crowded, and dirty in her view.
I'd not been there until we spent three days in Venice before a Rhapsody cruise last year, and she loved it!
I think the big difference is we were there together in late October, she was previously there in mid July!
I think Venice needs two days minimum, as do Florence and Rome.
Obviously, living in Ireland, Italy is more accessible to us, and we've been there a few times. My personal view is stay in Rome.