Trudy,
The Trenitalia website will indicate travel solutions with adequate time for changing trains.
There are two main routes you can choose, either via Milan or via Florence. I tend to prefer the Florence option. One of the quickest solutions will be a departure from Vernazza at 09:16, arriving Venezia Santa Lucia at 14:20 (time 5H:04M, 3 changes at La Spezia Centrale, Pisa Centrale and Firenze S.M. Novella). Two of the trains will be Regionale, so if you're using locally purchased tickets be sure to validate (time & date stamp) prior to boarding the train on the day of travel or you'll risk hefty fines! The other two trains are express trains (Intercity, Freccia), which come with compulsory seat reservations.
Some thoughts on each of the changes you'll be making.....
- La Spezia Centrale - you have 30 minutes for the change, which is more than adequate. You'll probably have to go down stairs to the Sottopassagio (transfer tunnel) and then back up to the platform your next train is departing from. Check the overhead display boards and look for the number of your next train. The track no. (Binario) will also be shown.
- Pisa Centrale - you have 15 minutes for the change, which again is adequate. You'll also have to haul your luggage down to the transfer tunnel and then back up.
- Firenze S.M. Novella - you have 15 minutes for this change also. Again check the display boards for your next platform and train. The change in this case will be very easy as there's no transfer tunnel. Simply wheel your luggage to the end of the platform, across to the next platform, locate your Car No. (Carrozza), board and find your Seat No's. (Posti).
Venezia S. Lucia is right on the Grand Canal. If you're planning to use a Vaporetto to reach your hotel, be sure to validate your ticket by touching it to the electronic reader before you board the boat. As I recall, there's a ticket booth to the left as you go down the steps from the rail station towards the Grand Canal.
There won't be any food on the Regionale trains. The Intercity may have a snack cart come through the cars with coffee and light snacks. The Freccia should have a dining car. If you decide to go to the dining car, it would be a good idea for one of you to stay behind to watch the luggage.
On that particular trip and given the long change time at La Spezia Centrale, I'd probably buy a Panino and beverage in the station and have that for lunch. As I recall, there are McDonalds at both La Spezia and Florence, if that appeals to you. Another thing I've done in the past is have my hotel at the departure point (Vernazza in this case) make up a small lunch. If you decide to take the train I've suggested above, you could also have a good breakfast at your hotel in Vernazza (if they offer one) and then have a late lunch after you've checked into your hotel in Venice. Lots of options!
