Avis rent a car in La Spezia is closed on Saturday.
Hertz rent a car in La Spezia is open on Saturday until Noon.
Europcar rent a car in La Spezia is open on Saturday until 12:30pm.
Hertz and Europcar are near the port, near via Fra Bartolomeo. very close to the freeway exit, so easily reachable coming from Tuscany. You will need to take a taxi from there to the station, because it's too long a walk.
I think returning the car at la Spezia is your best option, just make sure you make it there by Noon.
The drive from Siena is normally 2.5 hours, however on a July Saturday morning you will encounter a lot of traffic between Florence and the coast. Coming from Siena I would not go through Florence on a Saturday morning. Take the raccordo FI-SI (motorway) then exit at Poggibonsi Nord. After exiting the Raccordo, at the roundabout follow the directions to Certaldo. Once near Certaldo, follow the directions to Empoli.
Once near Empoli look for signs to the SGC FI-PI-LI (Strada Grande Comunicazione Firenze-Pisa-Livorno). It's a motorway. Follow directions to Pisa-Livorno. Enter the motorway (no tolls) and go toward Pisa. Stay on it past the Pisa airport until you get to the A12 Genova-Livorno freeway entrance (toll). Follow directions to Genova (Genoa) on the A12 then drive to La Spezia, where you will exit. From the moment you enter the A12 at Pisa to the moment you see the La Spezia exit is about 30 min drive.
Follow these directions and you should avoid a lot of traffic. DO NOT TAKE THE A11 -FIRENZE MARE on a Saturday morning in July. It will take you forever (and the A11 is a toll freeway too).
If your wife makes you late (women take forever to get ready) and you don't think you can make it to La Spezia by Noon (i.e. if you are not in Pisa by at least 11 am) when the rental car closes. Then exit the SGC-FI-PI-LI at the Pisa airport and return the car at the airport. The offices at the airport will be open all day Saturday. The from the Pisa Airport, take a shuttle bus to the station (5 min) and take a train from Pisa Centrale station (you'll need to change trains in La Spezia if you go to Vernazza).