The fleet building rules for a multiplayer Sector fleet battle indicate that each player chooses a set of 3 objectives for their fleet as usual; one red, one yellow, and one blue. But this would mean that, in a 2 vs 2 game for instance, that there are 2 sets of objectives potentially in play for each team. Then in the rules for objective choice in the Sector fleet rules, it says that the Grand Admiral for the first team picks from the 3 objectives of the second team. Have I missed a rule where it says how the second team determines which 3 objectives are being used for their team?

Just go Grand Admiral vs Grand Admiral.

Everyone picks their set in case the Grand Admiral hasn't been chosen yet.

From the rules, under Setup:

Quote

4. Choose Objective: The Grand Admiral of the first team looks at all three of the opposing Grand Admiral’s objective cards and chooses one to be the objective for the game.

The Grand Admiral choice is made during the Determine Initiative step, so you could be sneaky and try to pick the Grand Admiral you think will have the best set of objectives against your opponents.

Oh! I misread that. Totally clear now. It is the Grand Admiral’s objectives that get used.