Provence Itinerary Help

I'll reply with what I know from our last 4 days in Provence. A half day is definitely enough to visit Cassis. Unless you want the kids to do a bunch of swimming at the beach there? The first boats leave at 10:30. We got there a bit before 10 and found good parking. Choose the length of your trip, then you can have a coffee or whatever at one of the cafes...

July 16th sounds totally reasonable. Rousillon is a little hilly on the side streets, but the main road isn't too bad. Try to get a reservation at Chez David in Roussillon for lunch. We didn't, but it sounds lovely and is recommended.

July 17th. Lourmarin has a cute shady park between the castle/chateau and the old town. Great for some to stay and play while others explore.... (And there's ice cream across the street.) There's also a cute toy store in the old town. Fontaine de Vaucluse is so lovely at the top, but it's a bit of a hike/walk to get out there. Mostly paved. (We saw young kids out there.) We had a lovely lunch at a cafe along the way next to the river. There's also a pretty church in town I wish we'd had time to check out, and a "santon museum" (We checked out the one across from the roman arena in Arles and loved it.) Between Lourmarin and Rousillon is the Pont Julien, an old Roman Bridge that's stunning. We saw a bunch of families picnicking and splashing in the river here, so maybe it's worth a stop?

July 20th Arles. I'd consider adjusting your itinerary to start with the Antiquities Museum as suggested in the Rick Steves guide. It was wonderful to see the models of the town in roman times and really framed our visit to the town. We saw a few school classes there, so it's fairly interesting for kids. (My kids 5 & 7 would like it.)
There's a fascinating video about the roman barge they excavated from the Rhone... It's VERY handicapped accessible and modern (just one very doable ground floor). Maybe that, then the arena? Walking van gogh tour sounds like a lot for your dad and there really isn't that much to see in my opinion, just "the real version" of famous van gough paintings... we saw a couple and felt done... There's a cute park behind the arena and the ampitheater (it will just look like a lot of "green" on your map). We also bought some wooden bows and arrows here as gifts for our kids across the street from the arena that they love and are very durable... ;)

I do not see the Pont du Gard on your list, but it would pair nicely with Uzes.

Kids (and others) can swim in the Gard, if that appeals.

My kids enjoyed the bull games at Arles. Half the stadium is in the shade during the games - no problem getting a good seat.

I second the Pont du Garde. I also love the Roman ruins in Vaison-la-Romaine, the Medieval village of Les Baux (although a bit touristy) and the Roman Theater and the "other Arc de Triomphe," both in Orange.

And if you are able, you should begin many of your mornings with a visit to a local village market in the area. It's one of my favorite things to do in Provence. Usually in a week, we'll hit "le marché" in four or five different towns. They have wonderful food and local crafts, plus you get a real sense for village life. Often we'll put together a picnic of items purchased in a marché - local cheese, fresh fruit, country bread, sun-dried tomato spread, locally-made dried sausages, etc., and of course some local wine. St. Remy has a fantastic market on Wednesdays. You can find the schedule for markets all over Provence here, including the markets of many of the places you are considering visiting: http://www.beyond.fr/a/markets-by-day-all.html