There really is no way to guarantee space for three adults when using Priceline. Some cities (I'm aware of Munich 4*s) tend to do the two queen or double beds, but I don't think Rome is one of them. You are more likely to get lucky at the 4 or 5* level, but still no guarantees.
Several of the other other hotel sites like Expedia and Hotels.com and Venere let you put in # of people.
Another approach is to just get mom a single? Unlike the US, European hotels sometimes charge significantly less for a single than a double. Rome is not one of the better ones for that, but there can still be a price break.
There is
www.hostelbookers.com, and some inexpensive things are on there but they run a little primitive (bathroom down the hall, etc.).
You might ask in the Italy section about the beds in the IC? The IC is one of the main 5* wins for Rome, but again there are no guarantees a new/different one couldn't pop up at any time. You could also check betterbidding or biddingfortravel for reviews to see if people mention the bed configuration.
Romelle