Rome Hotels

In terms of location, I would put Hotel Lancelot last as it’s not “central” and would take longer to get to many sites. I have only stayed at Hotel Smeraldo but it was in a single room which was small-ish but had a balcony. Smeraldo has an annex across the street (that’s where Rick Steves tour stays) but I am not sure how big the rooms are. But it’s a great hotel.

Here is a previous discussion that gives a hint on the room sized in the annex.
https://community.ricksteves.com/travel-forum/italy/hotel-smeraldo-superior-double-room-parione

The annex is directly across an almost pedestrian only narrow road. Those who had rooms in annex reported they were good size. I was in a solo room that was small, but adequate, in the main hotel.

I walked through the area around Hotel Lancelot at least once, but in truth I don't remember anything about its character. I was staying in Monti, on the other (northeast) side of the Colosseum. I had a long stay in Rome, thus a long list of sightseeing targets. I was very aware of the distance of many of the key sights even from my hotel. However, how inconvenient a hotel is will depend on which specific sights you want to see. There are four quite major sights not very far from Hotel Lancelot: the Colosseum, the Domus Aurea, San Clemente and St. John Lateran.

Your closest Metro station to Hotel Lancelot would be Colosseo, on the opposite side of the Colosseum. Whether that Metro station or any of the sights I've mentioned are close enough for your mother to be happy walking to them, I do not know. You can ask for walking directions on Google Maps to see the distance and walking time (your mother will probably be slower than Google's standard). It's important to keep in mind that Rome is a hilly city. Hills can pop up rather inconveniently. As someone who walks around a lot throughout the day, I tend to sort of poop out when dinnertime approaches, so I really value being in a neighborhood with a bunch of decent restaurant options. I think I'd be satisfied with the possibilities in the area around Hotel Lancelot, but I've only glanced at the Google ratings, not the reviews or their menus.

I don't mean to suggest that Hotel Lancelot is your best option, just that I don't think its location is necessarily a deal-breaker. The Hotel della Torre Argentina is much closer to the Pantheon, which some folks consider close to the center of Tourist Rome. I don't see a nearby Metro station (though there could be one I missed), but in truth, the Metro isn't terribly useful in Rome. You'll probably use buses and trams more often, unless you decide to spring for taxis.

Have you looked for hotel reviews on booking.com? You can't leave a review there unless you've actually stayed at the property, which tends to keep the garbage postings at bay.