I don't have a specific recommendation for hotel near Avignon based on experience there but Relais & Chateaux and Small Luxury Hotels have great "collections" of independent hotels. Here are examples in or near Avignon. https://www.relaischateaux.com/us/fr...ve-lez-avignon or https://slh.com/explore-hotels?regions=Avignon. Enjoy the planning! And the marriage!

>>September 13:
Visit Chamonix/Mount Blanc (1 h 8)

One idea we thought of here.
We can either depart Annecy on September 13th afternoon at 4:44pm and arrive in Avignon at 9:17pm
(adding another night to Avignon) or depart Annecy on Tuesday morning at 9:00am,
where we arrive in Avignon at 12:42pm.<<

You have many more choices if you keep your car rented in Annecy and drive it to Avignon.
For your itinerary 2 nights Annecy, 4 nights Avignon you can leave Chamonix
with no rush to get back to Annecy to catch the 4:44pm train departure.
Or if you are back early you can just drive to Avignon with an arrival time earlier than the train arrival time.

For the itinerary 3 nights Annecy, 3 nights Annecy no need to take the 9am train departure. Just drive.
Perhaps leave Annecy at 7am and have a whole day of sight seeing before stopping in Avignon.
Potential stops enroute are Orange, Mont Ventoux, Cotes du Rhone villages such as Chateauneuf-du-Pape.

>> September 15:
Take a rental car from Avignon to Arles (44 m)
Take car from Arles to Camargue (19 m)
An option here is to cut the tour in Camargue for more time in Arles.
Spend the evening in Avignon <<

To me the Camargue is an all day trip. I would do Arles and Pont du Gard for a full day.

>>September 17:
Last option here: we can either explore Aix en Provence in the morning/early afternoon, or we can spend time in another, smaller area.
Depart either Aix en Provence or Avignon at 4:40pm, arrive in Paris at 7:50pm<<

I go for the smaller area. Perhaps Les Baux and/or Avignon's Palais des Papes and the nursery rhyme bridge.
Then drop off your rental car at the Avignon TGV station and off to Paris.

I second those who suggest staying in St-Remy-de-Provence instead of Avignon.

Avignon is just about perfect but if you really want to leave it then try Remy

St. Tropez is definitely a waste of time unless some glitterati friends have invited you to a party there.
The Camargue is a larger area than you probably think it is. Besides Arles, the absolute must is Aigues-Mortes, and Les Saintes-Marie-de-la-Mer is also interesting although not essential -- the drive through the Camargue is perhaps the most interesting part.

Here is my photo report about Aigues-Mortes: Aigues-Mortes (by kerouac2) | Any Port in a Storm (proboards.com)

My photo hosting site has turned some of the photos upside down for some reason. Maybe they will return to normal, maybe not. Sorry.

>>September 16:
Explore the Luberon/Gordes
Spend the evening in Avignon <<


If you really would like to visit Aix, how about this:

September 16:
Explore the Luberon. Take the route Avignon (or St Remy) to Gordes, Roussillon, Bonnieux, Lourmarin, Aix-en-Provence.
https://goo.gl/maps/384q1MjeTJ9eTdkD7
Spend the evening in Aix-en-Provence, Overnight in Aix-en-Provence.

September 17:
Explore Aix en Provence in the morning/afternoon.
Depart Aix en Provence TGV at 4:10pm, arrive Paris Gare de Lyon at 7:14pm.
There is another train leaving Aix at 5:18pm arriving Paris 8:30pm.