He's not supposed to be compromised the first time, because that story had nothing to do with the insecty things. It was supposed to be about a serious rebellion in Starfleet, without alien interference. The bug angle came later when Roddenberry didn't like the idea of renegade Starfleet officers. Which is too bad, because that would have been a much better story.
I wasn't aware of that change of focus, but the thing is, the viewer is invited to assume the two stories are linked, or at the very least there's no explanation provided to assume they aren't linked. So it appears that the starfleet rebellion is ultimately being controlled by aliens, which in itself is a pretty standard Trek plot twist. With that in mind, how and when and why Remmick got taken over is hard to explain.
Oh, and I guess on a point of order Remmick probably didn't get killed in the second episode. He was just a shell that looked like Remmick and the real Remmick must have been absorbed, or whatever, some time before. If there was any of Remmick left, Picard's actions are questionable, and they're pretty questionable even if there wasn't.