We went to Rome in September, we stayed just outside Rome in Ostia Antica in the walls of a castle, it was very, very easy to get into central Rome on the train and we were made very welcome. The restaurants in the village were very good and cheaper than eating in the city.
My Tips? if you want to go to the vatican, get up very, very early, aim to be in the queue by 8.30am at the latest. We got there later than this and the queueing time was approx 3-4 hours so we decided not to join it. Avoid the day when it is free to enter.
The Termini station area is not really very nice and we did feel uncomfortable round there but some of the hotels did look really good - I believe this is where most of the budget hotels are. I think if you are canny and be wise about what you carry you should be OK.
Don't have your picture taken with the romans outside the colloseum until you have agreed on a price (we got ripped of for 20 euros here)
Go to the churches. I am not really very religious but some of the churches are awe-inspiring.
I added a link to the vatican, there may be some information on 'audiences with the pope'.
http://www.vatican.va/phome_en.htm
Have a good trip! Your mum will love it, we want to go again!