I'm not blaming you for a spy being on the team, I'm accusing you of refusing to break up a team which then happened to have a spy on it, which is something a spy is likely to do.
That's just a hypothesis, given that this is only the second game, it's pretty hard to know what a spy would do. I could just as well assert that a spy could veto the team hoping that next one wins, and the spy gets to bask in some short term credibility. In fact, wouldn't a clever spy do the exact opposite of what the more obvious expectations are?
If you want to improve relations, skip your own turn. Skipping someone else's leader phase so you can go isn't going to help your cause.
But then any non-spies on a no confidence overturned team-potentially including the leader, would be just as frustrated, right?