for transportation, rent a car. Public transport in italy it's ugly. It's unconfortable, and a greate waste of time. Expecially if ur mum is "not young", i strongly suggest you to rent a car.
Anyway, if you plan to visit "big cities" like Rome and Florence, the car can be a problem. In Florence, you have to leave the car outside the historical center, and take bus (there is not the underground).
In Rome, instead, there is a lot of traffic jam, but there is the underground, so i suggest you to park the car outside the city, in the parking of a Metro station... usually, when i go to rome, i leave the car here:http://maps.google.it/maps/place?ftid=0x13...pn=0,0&z=16
You are far from the historical center, but you can easily park the car, and take the underground to mode inside the city. This metro station is called "Santa Maria del Soccorso".
I don't agree about Pisa... i have good memories, about it.
About Milan, skip it for sure.
About Siena, it's pretty.
I'd suggest you to visit Ravenna, it's full of outstanding churches with incredible mosaics. It's not far from Venice, just 150km south.
I don't know how about coeliachy.... but i recommend you to be very, very careful when in restaurants: be sure that the waiter understand your problem. Just a few, few restarurants, here, have the "special menu" for your problem.
Where do the painters go? strange question.... well, if you visit Venice, you can spend a day in "Comacchio valleys", in italian it's "Valli di Comacchio"... they are between Venice and Ravenna. You can google it to look some pictures... it's a good place to see waters and colours, and birds.
This is the only "interesting" piece of east-coast... to have a beatiful coast, on the east, you have to go south, and see the "Conero" coast, where i live... it's located in the middle of the east coast, so maybe it doesn't worth the distance.
I know that western coast, for example in tuscany, it's pretty, but i've never been there.
If you like to see natural places and parks, lakes, and falls, you should go either in "Umbria" (it's a region located north-east from Rome) or "Trentino"... Trentino it's a mountain-region on the Alps, and there are many beautiful places..
Anyway, in wich month will you come to italy?
P.S. sorry for my mistakes... italians are famous for bad english