If you drive, it won’t be much faster than a train. You need 3 hours, assuming you don’t get lost. And that is only the driving time, once you add the paperwork and stuff for renting the car and returning it at the Pisa Airport, and the transfer from the airport to the Pisa Centrale station, the train is faster.
12 min are more than enough to change trains at SMN.
The fact that the summer schedule for Regional trains is not out yet is not the amusing part. Those trains are subject to Regional subsidies which are negotiated between regional governments and Trenitalia, and sometimes those negotiations are subject to delays.
To be noted that Italian taxpayers are subsidizing those trains not only for their own local commuters, but also for foreign tourists who pay no taxes in Italy. I’ve always held the belief that local residents (taxpayers) should be allowed to buy discounted subsidized tickets and monthly passes on those regional trains, but non residents (non taxpayers) like you or me should pay the full price. The fact that Italian taxpayers are subsidizing your travels is indeed the most amusing part of the situation.