I have to say five things:
1) I (temporarily) live in Pisa, but i am from Firenze !!!!
2) V. Roma and Via S.Maria are not shopping roads. If you want a shopping
roads from the Duomo get Borgo, that is the third road on the eastern end
of the square.
3) I think you would better do the sidetrip to Pisa individually, more
time to go.
Upon arrival in Pisa get off the train from Montecatini at S.Rossore
Station. You arrive on track 2L . remain on that platform and look for a
tiny exit . You will be on the piazza del Duomo in less than 3' (if you
fell disoriented just look at the baptistry (Note that you begin to see
the monuments of the piazza, expecially the baptistry, from the train).
BTW: the archeological site where are digging roman boats is inside
S.Rossore station, behind track 3.
Then after visiting the Duomo/Baptistry you can walk throught via
Carducci-Borgostretto-under the lodges of city hall, the ahopping mall of
corso italia but just a side move to the tiny church of S.Maria della
spina. Then you can get back a train to Montecatini from central station
(last one is at 2043 mon to sat, 2140 on sunday)
4) About going to Firenze the day before the guided tour: I think it would
be better take a two hour tour on the first day, and the second day wander
orond, having seen the things you wanted to see better.
5) I agree in the suggestion about Venezia