You don't have to return to Innsbruck. Return the car in Austria (Salzburg) and take the train from there to Munich. The regional Meridian train runs from Salzburg to Munich almost every hour, takes about 2 hour, and you can do it with a Bayern-Ticket (no advance purchase necessary).
BTW, you didn't say from where you are coming to Munich. If it is from North America on a trans-Atlantic flight you don't want to book an advance purchase Savings Fare ticket on the EC because it is only valid on a specific train. If your flight is late, and you miss that train, you lose the ticket. Full fare (not train specific) on the EC to Innsbruck for 2 people is 89,40€.
You might want to take one of the regional Meridian trains to Kufstein. They leave Ost at 52 minutes past each hour and you can go from the airport to Kufstein with a Bayern-Ticket (31€ for two). The train ends in Kufstein. There you purchase an OeBB ticket (probably from an automat) to Innsbruck for 14€/adult and take the next train (any train, even a RailJet).
If you don't mind spending more time (2h51m), you could take one of the regional trains via Mittenwald (runs every two hours). It will cost 36€ for two with a "Werdenfels plus Innsbruck" ticket. No advance purchase is necessary; purchase at the airport. Via Mittenwald is a much more scenic route than via Kufstein. But the regional train to Innsbruck via Mittenwald leaves from the Hbf (Starnberger Bhf, Gleis 27-36, north side of the Hbf), not from Ost, so take either S1 or S8 from the airport to the Hbf.