It's too late now, but I think that if I were in that situation, I'd pick another restaurant to begin with. If there is any risk of your two worlds colliding with your wife present, why take the chance?
OR
You could have told her that you liked that restaurant, but that you've been there "with your friends" and if she didn't want to go there, you'd understand.
Then simply picked somewhere else after she gave the "hard NO."
I don't see where this is any need to "suck it up." There are plenty of restaurants out there. Just pick one you haven't been to as Steffie. It's no big deal.
I must say though, it bothers me that you're angry with her for not wanting to go there and risk it.
Please, please - respect her and her feelings, not resent her for them.