St.-Tropez has no rail service, so it would definitely not be my choice of a place to stay if I planned day-trips.
Southern France may be quite hot during your proposed travel period. Pay particular attention to comments in hotel reviews about the quality of the air conditioning.
I was in France during July 2017, and it seemed as if half the local population was on the same trains I was. There wasn't enough space on the luggage racks for all the bags, so I twice had to baby-sit my bag in the entry way of the car; so much for the reserved seat I had paid for. I recommend packing light so you can easily heft your bags onto the rack over your seats.
I think you're going to find that one night anywhere is close to worthless by the time you get a family of four to the new city and settled into a hotel. Be sure you've done some solid guide-book research before committing to just 2 nights in Provence. It's a very interesting area, and 1.5 days on the ground there is painfully short. Public transportation isn't quite as frequent there as it is right along the Riviera coast. A lot of smaller places have just very limited bus service, which makes it difficult to see more than one little town per day. The larger places like Arles and Avignon are not a problem, transportation-wise, but your plan for such a quick visit suggests to me that you're thinking of cute little towns instead.