Vienna to Salzburg with an overnight at Hallstatt at the end?

I would not rent a car. There are trains to Hallstatt from Salzburg and Hallstatt to Vienna. No need to go back to Salzburg.

Every Sunday there is one direct train from Hallstatt to Vienna (dep. 4:32pm, arr. 7:46pm).

Because on December 15th there is the yearly coordinated time table change of all railroad operators in Europe, all schedules on and beyond this date are still tentative and/or not yet published.

So the train connection mentioned above runs on Sunday, December 8th, but for dates after that there is no information available now.

You did not mention the exact dates of your journey.

@wmt1 the currently planned travel date from Hallstatt to Vienna is Sunday 12/22. I have searched and searched and did not see the information about the direct train!

The schedule isn't updated right now for that far out, but there are trains running all day long from Hallstatt to Vienna on every prior Sunday with a change in Attnang-Puchheim. There is rarely a dramatic drop of available trains on new schedules because Hallstatt is very popular. The reason to think about renting a car is possible bad weather in December and driving may be difficult. Obviously your choice. You can always make a free cancellation car rental reservation. Enjoy.

@threadwear yes! The weather is what makes this dicey with the car travel. I really would just rather do the train thing. I'm thinking we can just do the train from Hallstatt to Vienna with the changeover. It doesn't look too hard or too long. Just a little over 3 hours,right?

the currently planned travel date from Hallstatt to Vienna is Sunday 12/22. I have searched and searched and did not see the information about the direct train!

As previously said, all current train schedule information ceases on December 14th at the moment. The new 2020 schedule will be available mid October most likely. I don't see any reason that the direct train from Hallstatt to Vienna will be cancelled. In any case, there are several trains per day from Hallstatt to Attnang-Puchheim, where you can change to any high-speed train to Vienna.

Just for your comfort, this is the current train schedule between Attnang-Puchheim and Hallstatt and vice versa:
https://www.oebb.at/en/dam/jcr:1d1c904f-9daf-475f-b7fc-af65df29c3c5/kif170.pdf

Assuming your flight home is from Vienna - end there! On arrival in Vienna airport, go straight to the train station for Salzburg. After your nights in Salzburg, go to Hallstatt, then finish in Vienna. Saves that last random hotel night, and puts you in Vienna in case of bad weather that could make last minute transit difficult.