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Ok, this is weird. I did what you suggested, and it brought up my wife's contact details correctly.

When I say "call my wife", Siri replies with:

I don't have a wife number for "me". Would you like to use "my number" instead.

But if tell Siri to "call my wife's iPhone", it works as it should!

You might have a random contact place in your address book messing things up that you accidentally added
 
I had issues with Siri remembering relationships cause I was using google contacts syncing over exchange. Worked fine after I switched to the carddav protocol. Dunno if that would be worth a shot.
 
I've had this same problem with Siri regarding calling my son. I've added his name, told Siri who my son is, etc. Frustratingly, the problem is a random one that seems to come and go at a whim.
 
Are you using Google contacts by chance? I had the same problem for a long time- I kept telling Siri, text my boyfriend and then she'd go through the whole spiel, "Who is your boyfriend... Okay! I'll remember!"

But she never did.

Then I read an article somewhere saying you can only have custom names if you use iCloud contacts. Gmail has some system or another that only lets you sync certain titles - and a very limited number of them, like Boss and Spouse (not Husband and Wife).
 
I have my wife set as spouse and never had an issue. For fun I added a nick name to someone (who I won't give clues out in case they come here) a added b*tch. So I said call "B*tch" and it dialed that person name. I deleted it, I don't want to cause issues with this person :p
 
Siri won't ever call your wife cause, as you may have noticed, siri is trying to break up your marriage so you will start dating her. It's part of the whole plan....
 
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