Best way for a family of 5 to get from Montalcino to Vernazza?
To get to Vernazza by train you take a train to La Spezia and then get a connecting train to the villages. Vernazza (and the other villages) are foot traffic only. If Montalcino is a hill town, there may be travel by train and/or bus, but that could be difficult with a family.
I see Henry has already answered this on another thread here where you asked basically the same question. His advice, as usual, is spot on. The reason his advice is good is: the nearest train station to Montalcino is a 20-minute bus ride away in Buonconvento. As he advises, most people staying in the Tuscany Hill Towns rent cars. If you have one you can drive to an intermediate location, such as La Spezia, park the car at the train station, and continue by train to Vernazza.
You could also drive from Montalcino to Vernazza, but as Henry advises, many chooose to dump their rental cars in La Spezia. One reason why is that overnight parking in the CT can be a challenge. For day parking there is a parking lot at Vernazza, though it often fills up quickly from May to September.