You can add the Valensole plateau to see the lavender, but I would add an overnight stay. It is getting later in the season and higher elevations peak later. Moustiers St. Marie is one town, with Manosque on the other side. There are also fields outside of Dignes-les-Bains, a little further up. These are all a good 2 to 3+ hours away, one way, and you'll be spending a bunch of time in a car. I've heard, but not seen, the wild lavender fields above Grasse and Gourdon as you drive past some spectacular areas in the pre-Alps.
I agree, I would not add so many separate stays. Cannes and Antibes are separated by like 8 minutes by train (and Antibes just 15 minutes from Nice). Cannes can be just a day trip destination, unless you are going to add a ferry trip to the Lerins Islans just off the coast (Sainte Marguerite and Sainte Honorat -- the latter has more touristic attractions, a monastery with its own winery). You could cancel one stay and add the nights to an overnight trip further west and north.
There is a train pass available in the Cote d'Azur called the Pass Isabelle Famille. It's 35E per day and should cover your family. But you need to be travelling a lot on a train or pretty far to make it worthwhile. It is for the TER regional trains only.
https://www.ter.sncf.com/sud-provence-alpes-cote-d-azur/offres/pass-promos/pass-isabelle-famille
There are also day passes for individuals, per department, for the summer only.
There are attraction passes optionally bundled with bus/tram passes, called the French Riviera Pass. Choose carefully there, as the attractions need to really be worth it to offset the cost of the pass, and some offers may require advance reservations.