Just a few thoughts:
I think you are much better off flying from Paris to Venice than taking a train, it may be cheaper and will be much faster.
I flew that same flight on Vueling and think the flights were 40 euro per person one way ; definitely much less than an overnight sleeper train and that 90 minute flight is probably an 11 hour train ride! That is a huge time difference.
For the rest of your journeys the train makes the most sense.
Book the trains as early as possible is usually the best price just be careful as the best prices are usually not changeable/refundable.
Flights are usually best priced closer to your timeframe, predicting exactly when is impossible but if I had to guess I would say 90-120 days before makes sense.
August is not an ideal time for this trip but I assume your only option with the kids and your schedules for it to happen. Everywhere will be hot, not every place has AC, often encounter public transit areas without AC or hallways of steps without AC, it is just limiting on how much you can do in the heat. Not to mention the extra tourists at this time and in some cases either extra locals vacationing or the opposite with all of the locals gone and nothing but tourists like you in the touristy cities.
You are taking a very city and walking extensive trip. I would anticipate your children may have trouble or get frustrated by that. I personally like to break up any long trip to a mix of city and more of a nature area or less populated area where the place I am staying may a pool or similar for a little relaxation time.
With a 4 city tour of Paris, Venice, Florence and Rome (4 great destinations) you really don't have much time for additional locations but could do a couple of day trips ; expect to be walking many miles each day just to hit the highlights.
Cinque Terre I don't think works well as a daytrip, would be better as an overnight or there may be better options instead to do as a daytrip. Cinque Terre will be very crowded in August.
Of your 4 places I would recommending taking more care and being willing to spend more to stay where you want most in Paris and Rome. They are far larger so the location of lodging matters more, in my opinion. Venice and Florence are smaller and doesn't matter as much ; Florence is tiny so really doesn't matter ; Venice you can use means of transportation other than your feet to get around from so many places but do stay on the island for the best time.
