I've picked the most expensive option there is, OP, so that whatever tour you do decide on in the end will seem quite reasonably price
I've done a number of tours with Tauck (in their Bridges range meant for families) and the Italy one in particular was absolutely amazing.
This is their small group tour which includes Pompeii in a two week itinerary (hence the cost) and it also includes - as many of their Italy trips do - an after hours trip to the Vatican Museum, which is breathtaking. We had half an hour in the Sistine chapel just us and another Tauck group, with an expert guide explaining all the paintings to us, it was staggering.
However, this tour doesn't run in December, although Tauck do have their classic Rome, Venice and Florence one (which also includes the Vatican). I see that this day tour does, but on a limited number of days per month. So you may have to be patient looking for a tour that covers that exact dates you need in the off season.
One thing to note about a tour is that, although it's great that someone else does all the thinking and you just have to follow the herd from place to place, there is a bit of a social aspect to it so group meals may well be included. This might suit you - and I've never had a problem of being there as a lone adult with just my ds, someone will always invite you to join them (in Italy our tour group had a large party from one family so they were mad keen to talk to other people as they already knew each other so well!). I'm sure it'd be no problem if you wanted to do your own thing, however - esp on the night of the anniversary itself, when you might find you want the distraction of company, but you might not.
Hope you find something to suit - there is a very detailed description of how you do a DIY trip on the train to Pompeii, I will find that and post it in a minute. In my experience in Italy (and Belgium, Germany and Norway!) the high speed trains do their announcements in English as well as the native language, so it is surprisingly easy to do the train thing by yourself.