There is a major (in my view) issue with the two ticket solution. Should your inbound be delayed and you miss the first connection the flight back to Rome is likely to be cancelled because you didn't take the flight from Rome. Not only that but you'll probably have to buy a new ticket. Yes, I'm hedging with probablys etc; airline staff don't always follow airline rules!
The general rule is get off the plane, clear immigration (if applicable), collect bag, clear customs (if applicable) find the departures area and check in for the 2nd ticket, clear security, find gate, board. Two hours could be OK but at Rome ????