All teams are set up and ready.

Rebels win initiative.

Can they pick 1 objective and then give the other team the rights to go first and pick the rest of the objectives?

There might be a disconnect in the order of events here.

Initiative (first/second player) is decided before ships are set up.

Only one objective is selected for the match. It is selected by the first player, from the second player's objectives. (Each player brings one ojective of each color)

Brief recap of starting a game.

1) Players compare fleets (objectives still secret). Player with the lowest fleet point total decides to be first or second player.

2) Second player shows first player his/her objectives

3) First player picks ONE and only one of those.

4) Proceed to setup. Generally second player gets the first obstacle to place and the player alternate. The objective might specify a different way to place obstacles.

5) First player has to deploy first, then players alternate placing a ship or 2 squadrons.

There should be a step by step process that is more exhaustive near the back of your rules reference guide.

Ah!!! OK that explains it much better.

I thought you both had you 3. One of each type. Then played with 2 from second players set and one from first players set.

My friends and I have been playing with most of the optional rules. (We didn't change who goes first each round. So I started looking at the objectives after reading that they help balance things.)