It might be damaging, but it'll be the hospital paying a smaller sum than it would be worth in the end. Then they'll just pass the lawsuit onto the people that pay their bills there. It's like suing the local government, the tax payers pay the lawsuit money. Also at most the receptionist would get fired, and maybe an apology of some sorts in the newspaper.
It sucks OP will have to deal with possible divorce, rehab, etc. but it's better than trying to deal with that all and losing money on a lawsuit.
Even if OP wins the hospital lawsuit, he'll be drained from it and good luck trying to save a marriage after "winning" a lawsuit against HIPAA regulartions. From what it sounds like, OP might get a few thousand in the end, after a year or more in court off and on. HIPAA related lawsuits take so long, and only worth if if it's major.
Accidentally giving one person extra information, that's seen as a spouse is not much compared to someone stealing patient info and selling it to someone else. That's what they want more than anything, and that's when big money comes in. Accidents like OPs do happen a lot with medical institutions.
Any lawyer will take the case, but I'd be surprised if it goes anywhere. The lawyers will pretend it'll go far, just so they get paid. Ask a lawyer to take it pro bono because it's an open and shut case, and they'll laugh at you.
I worked with Law Enforcement and Hospitals in a previous life. I've gotten subpoenaed a few more times than I should have. It's all so fucking stupid. I've seen HIPAA lawsuits from something that affected 7000+ people, and not a single lawsuit went beyond the 2nd day in court (even at completely different courts). A handful of different people tried to sue the hospital for various unrelated HIPAA related issues, but lost and ended up paying the lawyers in the end. HIPAA is a fucking joke due to how grey it is. It is not this black and white law. There's very few things in HIPAA that are unfortunately.
Sorry OP, but if you sue, good luck! You'll need it, but it'd be easier to be honest with your wife at this point, if she's worth it.