Siena-Orvieto-Rome

It's doable, although I don't know when this night tour starts. But yes, it's a bit rushed, so you won't have a lot of time to linger in Orvieto. Start early in the morning so that you have at least 3 hours in Orvieto.

I think Orvieto is very safe but I haven't been there for years and I don't remember the parking situation. Just don't leave the trunk contents exposed.
As far as returning the car in Rome, many people in this forum don't feel comfortable driving in Manhattan type traffic typical of large European cities. I don't know how you or you spouse feel about city driving, but if you don't feel too comfortable choose a drop off office near the Tiburtina Train station, which is close to the freeway exit coming from the Tangenziale Roma Est (A24). I generally return it at the Termini station, which can get really chaotic at times, but I'm familiar with big city driving in Italy (and often drive to downtown San Francisco to work).
Whether you should do Orvieto on another day or not, depends on how much time you have in Rome and whether you would like to spend more than just a few hours in Orvieto.

We lived in San Francisco for years, and are used to big city driving. But we know SF, and we don't know Rome, and I can just see some stressful times ahead. Is Orvieto worth more than a few hours? I hate to be one of "those" who do a city in a few hours, but since we are driving right through it I thought it might make sense, unless it's worth it for a separate day trip. We will be in Rome Friday evening (for the Vatican tour), Saturday, Sunday Monday, Tuesday, and leave on our plane Wednesday morning. One of those days will be a long day seeing Pompeii (at least at this point), so I think I may have some spare time.

Anyone else on here park their car in Orvieto and think it was safe?

We drove from Montepulciano to Orvieto where we dropped our car and then took train on to Rome. You would need to leave Siena early to do this. There is free parking behind the train station and we left our luggage in the car while we toured Orvieto but we had a trunk so it was hidden. We were only able to spend a few hours in Orvieto because the Hertz rental office closed for an hour at 1pm and we wanted to take a early afternoon train into Rome. In that short time we were able to see the Duomo which is truly magnificient and grab a panino. No time though for the Etruscan tombs or St Patricks well. If you do this be sure to first check the times that the car rental is open and the train schedule. The car rental, train station and funicular are all very close together so this is a timesaver.

Orvieto is a very easy train ride from Rome, it may be less stressful to do a daytrip rather than counting minutes so you can get to Rome on time. Depends on how many days you want to spend in Rome.

In Orvieto, the Duomo is spectacular, entrance is free (no entrance during Mass times), but buy the ticket to see the Signorelli frescoes up close. Orvieto is a beautiful town to wander in for a few hours. There are several churches (the oldest is San Giovenale, recently restored and reopened), beautiful views from some of the terraces, and a hair-raising ride on the mini-bus that does the circuit all through the town (not the one that goes from the funivia to the Duomo only). Saint Patrick's Well is on one side of the funivia station, the ruins of a castle are on the other side.

Driving from Siena to Rome on the motorway takes about 3 hours, which I think does leave enough time for a stop in Orvieto. Luckily, the sightseeing does not close for lunch, although the tourist office does. If it's Sunday, pay attention to church times. For motorway toll estimates, see www.viamichelin.com.

By train through early June, the 15:23 regional departure from Orvieto arrives in Rome about 17:00 and 2nd-class ticket prices are €7 per person. Or earlier, an InterCity train departs Orvieto at 14:10, arrives Rome 15:20, and costs €17 per person in 2nd class.