If I were her, I would have been annoyed at you for getting pissy rather than just straightforwardly expressing your desire to meet the guy and/or that you didn't trust him. After all, I'm not a mind reader, how can I know why you're being pissy, all I know is that it sucks! So, good on you for figuring it out in the end and telling her. And good on her for listening and suggesting the coffee date. Aaand, it looks like you were right to be worried, since it freaked him out!
Next time, talk calmly about your feelings earlier, even if just to say "I have a bad feeling about this and I'm not sure why, would it be possible for you to wait a couple of days before your next date so I can work it out?" Getting pissy is never the right answer, especially since your wife sounds like a reasonable person.
Of course, you could also request a guideline along the lines of "Don't have dates with the same person more than once before I get to meet them"? But I doubt that's the real solution, since a variety of other issues could come up that would similarly put you in a position to feel bad/weird. Better to work on the communication overall.
The major players. Me, under-30 bi female. Gia, girlfriend of 3+ years. Clay, new boyfriend/dom. Davis, ex/"it's complicated."
The supporting cast. Eric, Gia's husband. Bee, Gia and Eric's toddler. Dexter, Gia's lover. Helen, Eric's lover. Izzy, Clay's partner.