Hi Bart, I don't have any specific accommodations to share with you but can recommend some tour companies. I'm actually heading there in less than a week with a friend and the kind people on this wonderful forum along with reading RS's Italy guide book helped. I discovered that in RS Italian guide book there's a section specifically listing tour companies or guides for each major cities. Take walks is a pretty popular company and I'm doing two of their tours in Rome: the Pristine Sistine and a coliseum tour. ttps://www.takewalks.com/rome-tours/ There's other tour companies out there that RS list in his book. For Rome most everyone has suggested that you stay in the Pantheon area of Rome because its easy to walk to most sites. If your 80 year old mom has no issues walking then maybe you won't need to take a Taxi or public transportation much.
Once you have your dates if its not to far in advance I suggest you go ahead and book your train from Rome to Florence and back. I'm made the mistake of not going ahead and booking sooner than later for a couple of my travel legs. Some trains are booked so then you need to leave earlier or way late.
The Florence Pass/ card which is not available at the moment anyways, isn't worth the cost unless you went and saw lots of the museums offered on the card. In most cases your not saving much $. For the Uffizi and the Accademia Gallerias you can either pay and go with a tour company that will show you the highlights or you can reserve your own time slots and go walk the museums yourself. Going earlier you avoid crowds in theory but It depends on what time of year your going. If its during wintertime then it won't be an issue unless it was say at Xmas or some holiday. https://www.uffizi.it/en/visit https://www.uffizi.it/en/tickets.
You and your family will have lots of fun when you go. For my 3 week trip with my friend I've planned it so we have just one reserved activity or less per day. Some days we have nothing specifically planned so we can just walk around and do whatever we want. I haven't booked it yet but also still deciding if we have the time. In Florence you and your family might enjoy taking a Pizza and Gelato making class. IF your teenagers like to cook or make pizza. There's also food specific tours if people love food and you might enjoy those. There's various places where people offer cooking classes.
Lastly and I didn't know this don't use Viatar to book any tours etc. I found out from people on here that it is a 3rd party website and you don't know what type of tour you'll get. Its better to just book directly with a company and give them all the money. Have fun and hope some of this info help. Other then my personal opinion most of what I wrote was info shared to me on here so I'm just repeating what was told to me. Buon Viaggio