I regularly drive to Florence from Basel and I must say that in winter the Gotthard is not too bad and from Rotkreuz I would go directly to Milan. Traveling via San Bernardo Tunnel is not only by far more distnt, but also much slower (as the last part in Switzerland is not a motorway). The motorway from Genova to Pisa is not as stright as the other one. Milan to Bologna is straight 3-4 lane motorway, not a big hassle. Bologna to Florence can be a bit busy in the final part, expecially from Roncobilaccio to Florence. But I must admit that in the last year the economic crisis in Italy has cut the lorry traffic drammatically.
We travel with a small kid and we usually stop over, but it is feasible in just one stretch. Parma, Modena and Reggio Emilia are all nice little cities, worth visit to a restaurant for local specialities. Culatello, filled pasta ravioli, etc.
For reliable weather forecasts in the area, you can use this: http://www.lamma.rete.toscana.it/en/meteo
Enjoy Rufina and have fun.