It was a rental car, so I think she had two sets of keys. I agree though, the editing of the whole sequence was really botched.
The whole episode was sloppy.
Mendelsohn's wife guilt trips him because Holly leaves the house in the morning. This is not a normal reaction for his wife to have. Then, through 5 minutes of plot contrivances Mendelsohn concludes that she was kidnapped? Holly could have left Mendelsohn a note that she was going out with Jack (rogue cop) to follow-up on a lead, but also asked him to please call her once he is up and going for the day.
The cop that Mendelsohn answers to, the guy that wears the GBI vest, all of a sudden is once again interested in the Strip Club manager? Why? What possible reason would GBI vest guy have to be circling back around on this guy at this point? Mendelsohn hasn't even learned that the guy has quit yet. And even if he has quit his shitty strip club manager job, who the fuck cares? Unless, we need to bring this non-essential character back into the story for a "gotcha" moment later on. Thus the freak-out by Mendelsohn's wife about how he was scratched by Terry Maitland and now everyone needs to find this guy ASAP. So contrived...
It was a good moment in Ep 6 when Holly confirms Jack is compromised when she gets him to lean forward and sees the boils on his neck. Then, this episode, Jack just comes right out and shows her? He goes from being uncomfortably mute to spilling his guts on how a demon possessed him? Then, when Holly gets away, he pulls out his gun and starts popping off? He just went from plausible deniability about the whole situation, to attempted murder in a very low % chance of taking her out. Not something a cop would do.
From later dialogue, we know that they are 2 hours in a random direction outside of town. Not near the farm house or anything. We see Holly peeling out of the gas station in a completely random and frantic direction, and then Mendelsohn & private investigator dude at the same gas station and indeterminate amount of time later. They inspect her destroyed phone. They go from being scattered all the fuck around in random directions at different times at a minimum of 2 hours out town, to being back together in Mendelsohn's dining room. No communication, no coordination, just back home. Even the lawyer, who wants to sue all their asses is there like a big happy family reunion.
So many elements in this episode fail the logic test. HBO is supposed to be better than this.