FCO Airport Logistics

This looks to be separate tickets? It’s too tight of a time frame for this “connection”. Some Alitalia flights at FCO don’t disembark via a jetway. They use a bus to get you to the terminal. This can add 10 to 15 minutes. So even if your flight from Turin is on time you may not be in the terminal until 8AM for a 9:15 flight.

I did something similar coming back from Sicily. I left 4+ hours between scheduled landing and departure times.

I would get to Rome the day or night before. Way less stressful that way.

I would want to be in the city my international morning flight leaves from. To many places for things to go wrong sleeping in another city.

I too would want to come in the night before and stay at the Hilton Garden Inn Hotel on the airport property.
Another option might to be to fly home from Italy's #2 airport--Milan Malpensa. It's closer to Turin.

If these are separate flights, I would not want less than three hours connection time, and that's only if you like to live dangerously.

You need extra time to go through exit immigration and, of course, security, in Rome. It is too tight if two separate tickets. If it is one ticket - connecting flight in Rome - then it maybe OK. However, is the 9.15am flight a direct flight back to the US or does it connect to another flight in Europe? Generally, direct flights to the US are later than 9.15 -- closer to noon and early afternoon. If it is a connecting flight to another city in the Schengen zone, then the time is probably adequate since you would not go through exit immigration. Need to know you exact flight details.

I see an AA non stop to Dallas (DFW) departing at 09:15 on May 20.
The problem is that boarding for those wide bodies start at least 55 minutes before departure and the flight closes no later than 15 min prior. That means that boarding starts 25 min after your arrival and closes by 9am. If the plane is on time it is doable but if not you might miss it and if you are on two separate tickets AA may not be liable and you’d need a new ticket. If it was all Alitalia with one ticket then it would have been no problem. They would have rebooked you in case of late arrival.
You do have to go through an extra security check in Rome and also passport control.

"If these are separate flights, I would not want less than three hours connection time, and that's only if you like to live dangerously."

I agree. What are the consequences if you miss the flight back to the US? You would have to find another flight back to the US, and pay for it at last minute prices.

Yes, flying in from Turin on a separate ticket, you will have to go through both security and passport control in FCO.

So, "Would it be better to fly in the night before, rent a hotel and fly out in the morning?" For me, that's the only way I'd do it, with such an early intercontinental departure. I had to do this when going from Sicily back to the US through FCO on separate tickets. It may feel like a bummer to have to do this, but not nearly as much as of a bummer as it will be to miss your plane!

Note that there are two Hilton's near the Rome airport. One, the Rome Airport Hilton, is connected to the terminals via a walkway that takes about 10 minutes. The other, the Hilton Garden Inn, requires a bus ride to the terminals, but is substantially cheaper.

. Is 1 hr and 30 minutes enough time to land on Alitalia and get to and American Airlines flight?

I would put odds of success at no more than 1% ( on a good day)

Would it be better to fly in the night before, rent a hotel and fly out in the morning?

ABSOLUTELY