Dijon to Avignon Train Confusion

There are only two train stations in Avignon: Gare d'Avignon Centre, located right outside the historic city walls, and Gare d'Avignon TGV, on the outskirts. It sounds like you would prefer Avignon Centre as you are actually going to Avignon city.

There are no nonstop trains from Dijon to Avignon, either the Centre or TGV stations. The best choice in your situation is to pick a 1-stop itinerary, which will having you changing trains in Lyon as you saw. In other words, Dijon to Lyon and then Lyon to Avignon Centre.

There are a number of 2-stop itineraries that mostly seem to have you change trains once in Lyon and once at Avignon TGV. There's no reason to book these, especially because in most cases the travel time is longer anyway.

The fast trains stop at the Avignon TGV station, not at Avignon Centre. So you have a choice of taking a slower train (TER) and going more directly to Avignon Centre or spending some time on the very fast TGV but needing a shuttle train to get you to Avignon Centre (or a taxi, but that would surely cost more). As far as I can tell, you are correct that you'll need to change trains in Lyon in either case.

If you look at all the options (use SNCF so you can also see the fares; do not use RailEurope, which will cost you more money and may not show you all the available trains), you will see some variation in the travel time. However, the routes that include some time on a TGV are not necessarily substantially faster than those that have you only on TERs. That's because you may lose as much time on your layover in Lyon (or at the Avignon TGV station) as you gain by making part of the trip on the much faster TGV.

Another thing to note is that any routing that includes a TGV will cost quite a lot more unless you are buying very early and are willing to buy one of the bargain-priced non-refundable/non-exchangeable tickets.

I don't know when you're traveling, but I think it's unlikely a rail pass will save you money. You should price out your three trips, using your planned travel dates to see what you'd pay if you bought the tickets today. Then look at the same trips for tomorrow. Are they a lot more expensive? That shows you how much you can save by buying early and committing to a specific train. If you're not sure about your itinerary yet, you'll need to wait and hope the fare doesn't change too much in the meantime.

If you can't find tickets for your dates, they probably aren't on sale yet. In that case, look for prices as far out as you can go, using the correct days of the week (based on your current planning).

Edited to add:

I would prefer not to have a really tight connection at Lyon Part Dieu. That is a very large station, and when I went through it in 2017, the concourse was quite crowded. There was a fair amount of bobbing and weaving necessary to work your way through the crowds, though I'm sure it's not always quite that busy. There's no sense in insisting on a very long layover in Lyon, however, because they won't post the track number of the train to Avignon terribly far in advance. I think it might be about 15 minutes. As I recall, access to the tracks is via escalator, so at least you don't have to drag your luggage up and down a bunch of stairs.

Rail passes not as good a deal as they once were, but maybe.

If you are going to ride the TGV, note you must purchase a reservation even if you have a pass.

Lyon is the direct route, it is the rail hub between Dijon and Avignon.

You can change either in Lyon, Nimes or Valence, depending on the train and the time of day, and spend anywhere from 3.5 to 5+ hours in transit. Try to buy the ticket that includes the Avignon TGV to Avignon Centre leg, (i.e. make sure Avignon Centre is your final destination) so you don't have to fumble with a ticket machine while rushing to your last short connection into town.

https://en.oui.sncf/en/results/?wishId=5c760380df35851172a1329d#!/?queryId=Xcbrr

I wouldn't even buy a ticket that had an Avignon TGV-Avignon Centre last leg to begin with; just find a 1-stop itinerary from Dijon to Avignon Centre (most involve a change in Lyon) all on regional trains.

Opting specifically for the TGV in this case doesn't make much sense because it forces 2 connections and because the travel time and price savings don't appear to be significant. So if travel time and price are roughly the same, you might as well go for a 1-stop itinerary, which will avoid the Avignon TGV-Avignon Centre shuttle entirely.

The connection between the old central station and the TGV station on the edge of the city is a shuttle taking approximately five minutes. However the website counts it as a connection. The old route on the TER from Lyon to Centrale can be more scenic than the TGV but is certainly slower and perhaps less comfortable. Not everyone wants to ride at high speed, of course.
The fast train route was a complete construction project with dedicated new tracks that often included a new station on the outskirts of cities (but not all of them.)