Rome in late November

The last time I was in Rome was November 11-15, 2012. The weather was nice and we had high temps near 70 every day. The only caveat is that daylight savings time had ended, so it got dark around 5:30-6:00. Most sites closed earlier as well. The crowds were more than manageable. In June you will have more daylight and longer operating hours for most sites. If you get reservations for all of major attractions, crowds will be manageable. Early June is better than late June.

One other consideration: there is plenty to do after dark in Rome. The Trevi Fountain, Spanish Steps, and other attractions are open 24x7. It's nice and coll for those evening walks!

November versus June in Rome? Hmmm. Normally the general rule of thumb advice is not to go to Rome in the summer, if you don't have school age kids or some other reason why you're forced to go in the summer.
November is a little late in the season but since you say you have low weather standards, it might be better than June.
You ask if Rome will be "super crowded" in November--No, not super crowded, not compared to June or some other months I could name.
If you go in November, you'll have significantly less daylight so your outside sight-seeing will be over much sooner than June, you can get the details on that by going to the same weather site you've apparently already looked at.
If you go in June, pay extra for a room that you are sure has AC (not all do there, it's not like here in that respect).

I've been to Rome in November and in June, I prefer November because of fewer tourists. To me, that makes up for the shorter hours and possible chill. It will not be freezing in November, but pack for layering and take something for rain.

Weather is a dice roll. We were in Rome the first week of June two years in row. For three days the first time, I thought we were going to freeze. It was so cold the sidewalk cafes did not open. The next year we baked. Remember, to have an average, you live the extremes. I would prepare for cool, damp, and probably some light rain and be very pleased if it is sunny and warm.

I used to go to Italy at Thanksgiving almost every year. Typically the weather in Rome would be exactly the same as where I live (SF Bay Area). Florence, being farther from the coast, would be a bit cooler ( like Sacramento, CA).

I would go in June just because of the age of your children. They would probably enjoy the weather more and be more willing to stay up a bit longer at night. Remember that dinner doesn't begin there early in the evening.

Hello,
I was in Rome over Thanksgiving a few years back. It was definitely cool and there were a few rainy days. The trade off for the so so weather was less crowds. For instance, we went to the Vatican Museum in the afternoon and got a seat in the Sistine Chapel right away. I would definitely go again over this period but just plan for chilly grey/rainy days. . . which are perfect for spending hours in museums!

I was just at Rome in late November 2014 and it was warm T-shirt weather during the day, a few days cloudy and some light rain where a light jacket and hood may help. I would have lightweight rain gear with me and light jackets with hoods. It may get cooler at night.

The free App
iL Meteo
shows temperatures and weather conditions in Italy for two weeks in advance. Check before you leave. Just double the Celsius number and add 30 for quick conversion to Fahrenheit.

My husband and I were in Rome Nov 13-17 2014. The weather was in the high 50's-low 60's during the day and obviously cooler at night. We did have some light rain and one night we had moderate rain. However, overall we thought the weather was great and would go back in Nov again. We made sure we had an umbrella (there will be people selling them in the street as soon as it starts to rain) with us just in case. The best part of being there in Nov was that there were so few people. We had purchased tickets online for all sites we wanted to see, but there were only short to no lines for those who hadn't. We didn't have problems with crowds at all. I think this allowed us to enjoy our trip even more. I too was worried about the dates I selected and checked the weather multiple times per day before we left. Please don't be discouraged or torn if you really want to go in Nov, I'm sure it will be fine and you can enjoy the sites even more.

Thanks! I think I've decided on June, but if you see me here asking about my November trip, don't be too surprised :) I'm a little indecisive. I want to go ASAP but I'm 99% sure I will wait. June will work better for us for several reasons.