Munich to Salzburg
I think your best bet here is one of the hourly regional (BRB RE5) trains. These train originate in Munich Hbf and end in Salzburg Hbf, so there is plenty of time to board (assuming you get there well before departure time) and to get your luggage off on arrival. Leave from the Munich Hbf; these trains only stop for a minute at Munich Ost.
With one of these regional trains, as long as it is after 9 AM workdays, you can use a 36€, two adult Bayern-Ticket. Both children will be free, but I think you need to name the free 8 year old on the Bayern-Ticket.
Next best (albeit more expensive) is the RailJet (RJX). It originates in the Munich Hbf and stays for 9 minutes at the Salzburg Hbf, which should be enough time to get all of your luggage off.
I wouldn't use an EC, which originate farther west in Germany and don't have much time in Munich to board. I also would not use a WestBahn train, which is only scheduled to stop for one minute in Salzburg.
Salzburg to Vienna
This gets a bit more complicated depending on whether you want to go to the Vienna Hbf or the Vienna West Bahnhof.
The West Bahn goes to the West Bahnhof while the RJs go to the Wien (Vienna) Hbf. There is a streetcar between them. With the luggage you have, taking the streetcar between stations might be cumbersome. Best advice, if you are staying near the West Bahnhof, use West Bahn. If you are staying near the Hbf, use an RJ.
Some of the West Bahn originate in Salzburg and end in West Bahnhof, so you would have plenty of time to board and get off. However, other West Bahn originate in Munich and only give you a minute in Salzburg to board.
As for the RJs, there is too many variations to try to cover here. A few RJ originate in Salzburg and end in Wien Hbf. Those ones would be good to take. Others start in Salzburg (good) but go on to Budapest with only a few minutes to get off with your luggage in Vienna (not so good). Some RJXs start in Munich and only stop in Salzburg for 9 minutes. Some of those end in Wien Hbf while others only stop there for a few minutes and go on to the airport.
You just have to look at each connection and decide if it give you enough time to board and get off.