When I bought my train ticket from Lyon to Aix-en-Provence I selected Perrache station because it was closer to our hotel. I ended up with one ticket from Perrache to Lyon Part-Dieu and a 2nd ticket from there to Aix. But there are only 12 minutes between arrival and departure in Part-Dieu ... IF things are running on time. This sounds worrisome! Should we just take a taxi (well ahead of departure time) from the hotel to Part-Dieu and throw away the ticket between the two stations? Or would that cancel our reservation out of Part-Dieu?
Just stick to your plan. You will be protected if the first train is delayed. 12 minutes is plenty of time.
If you are worried about the time to change, spend a tiny bit more money and get the tram from Perrache to Part-Dieu, leaving a bit earlier.
You do not say the date and departure time, and if you are going to Aix-en-Provence or Aix-en-Provence TGV. If the 1st train is a TER, you can just take an earlier train. If it is a TGV, it originates at Lyon Perrache and should leave on-time and is is only 9 minutes to Lyon Part Dieu, so unlikely to be delayed.
It's the TGV station in Aix.
When you say "originated" does that mean we DON'T change trains in Part-Dieu? The first ticket has no assigned seats and the 2nd one has reserved seating.
Originate means that the train starts there, Lyon Perrache. It is not coming from somewhere else where it can get delayed. You have not told us the time or date, since you say it does NOT have seat reservations, I can assume it is a TER. Let me guess, 11:20 am? If you are worried, you can take the TER at 11:01 am. That does not originate at Perrache, but at another Lyon station, so should be fine. TER trains you can take anyone that day on that route. So if you took that one, you will have about 30 minutes at Lyon Part Dieu. Time enough to get bored.