Up to the wingee. So yes, the wife should "get over it", it that's what the pilot wants. Even if he wants it because his dad is making a big deal out of it, it's his decision and he's welcome to use whatever criteria he wants, even if that criteria is bowing to pressure from dad.
It might well be perceived as a slap in the face to the wife and might make her feel less appreciated, but that's on her. And doesn't bode well for the future.
DH's winging happened in a blur. (He volunteered to be winged at NHA because it was near our family's hometowns, so he didn't wing with his class and we had a crazy quick move.) I hadn't though to ask him, and when he went up there, I asked his mom if she wanted to do it. She quickly and adamantly deferred to me (fiancee at the time), which I suspect would have been what he wanted as well, so I did it.
Really, if you (er...global "you") don't do it, what does it matter? Does it make your contributions to the process any less (or any greater if you do pin)? This moment isn't about you--not even a tiny little bit. Let him choose, and when you ask what he wants (if you have to ask; maybe it is already clear), do it in a way that makes it very clear you are open to his decision and that makes it very easy for him to give you an honest answer. Let him know you are fine with whatever he decides (and try your hardest to actually mean that) and that you respect his decision and are proud of him, no matter what.