Hi Bridget,
Here is a list of tour companies that you can view and compare. They pretty much all get good reviews and have similar itineraries. You can also see on their sites the maximum number of people they will take.
Look for discounts on their sites or if calling, inquire about discounts.
https://theromanguy.com/
https://www.walksofitaly.com/
https://www.througheternity.com/
https://darkrome.com/ (Dark Rome and City Wonders are sister companies)
https://citywonders.com/
https://angeltours.eu/destination/rome/
Keep in mind the time of year you will be traveling. Of course, high season will have abundant crowds, long lines in some cases.
Also, to get an idea of Rome's city centre and vicinity, check out the YT version of The Roman Guy.
https://www.youtube.com/results?search_query=the+roman+guy Scroll through to view; especially the "neighborhood series." They have a lot of great suggestions and tips for the newer traveler. Sean, who is one of the company's leads, narrates most of the vids.
Keep in mind It is always encouraged to check out the original websites of any suggested attraction - times, dates, closings, pricing, policies may change at their discretion.
Places like The Vatican, St. Peter's will have a security check - no large bags or backpacks in either. Bags of about 14-15" were allowed all the times I went to St. Peter's. So far, it has not changed.
There are very strict rules for no photo taking in The Sistine and St. Peter's (Chapel of The Blessed Sacrament.)
Strict dress codes are enforced especially for The Vatican and St. Peter's & most Churches.
If your Mom will be using a walker or cane for when she may tire, they are allowed at main attractions. They will be put through security at The Vatican, St. Peter's, The Colosseum, and The Borghese Gallery. I saw strollers in St. Peter's - no large baby carriages (prams)
The Colosseum was allowing bags of about the same size as above. The Borghese Gallery at one time did not allow any bags of any size - plastic totes were given out to carry wallets, phones, etc. Now, they have allowed small sized bags - 8"-9" in size.
Other churches in Rome are not as strict with bag sizes.
You will probably visit The Pantheon - it is an active Church and its history is astounding. https://en.wikipedia.org/wiki/Pantheon,_Rome Piazza della Rotonda is very active and fun.
Piazza Navona is gorgeous with its flowing fountains. There are concrete benches to sit and rest a bit. Grab a gelato - enjoy, sit and admire the beautiful and awe-inspiring fountains.
Fontana di Trevi is magical - especially at night.
Piazza di Spagna (The Spanish Steps) and Trinità dei Monti (Church at the top of the stairs)
Altare della Patria / Piazza Venezia - Stunning and crazy busy.
Check out the https://www.skylinewebcams.com/en/webcam/italia/lazio.html
Each one gives a bird's eye view of major attractions, piazzas and so on. You will get an idea of people crowding, what each area looks like at different times of the day. Sometimes they switch out the cams - usually Campo de' Fiori is up and running for day and night viewing. It is a lively plaza for sure.
Check out https://www.romewise.com/ Elyssa is a Rome resident for many years. She is very knowledgeable and super nice.
Have fun planning and traveling to Rome! People in Italy are so nice and helpful. I have made friends from my first trip years ago. When I visit now, it is like I never left, lol. I love it!
adding You may know this already but schedule wheelchair assistance at all airports on each leg of flights. Airports have an express line of sorts. She will still have to go through the usual security. At least she won't have to stand for a long time. She will have an airport escort but you can walk along with her and then go through the regular line.