Our daughter was almost 4 years old and still not potty trained. My then wife would say she wasn't ready. In reality, she stayed dry all night since she was 18 or so months and first thing in the morning, she would go in the corner behind her doll house a pee and poop in her pull-ups.
The bolded reminds me of our oldest child. At 3 he would peepee in the potty but refused to poop there. Instead he would back up to a wall and poop in his pullups. I'm not sure why he bothered backing up to a wall, but I think he thought he had privacy there?
When we put him in cloth trainer pants he held his poop for 4 days until we had to give him an enema in the tub. (Dr. recommended)
He hated that AND SO DID WE! After the 2nd enema he decided he would rather poop in the potty. I think it was a control thing, because he grew up to be very stubborn.
Our 3rd child potty trained herself at 2. One day she decided she didn't want to wear pull-ups anymore and put on her training panties instead. She had one peepee accident and changed her panties herself!
Children are people and they are all very different.
With regard to your daughter, I don't know any 12 year old (who has all their faculties) who still pees and poops in their pants. She will learn sooner or later.
With regard to your wife, tell your wife that if the two of you can't get on the same page, then she had better let you know when she is not going to be around whenever she puts your daughter in panties, because the next time she puts her in panties and takes a nap or leaves and your daughter has an accident, your wife is going to find dirty panties on top of her own pillow. If that is too drastic, then think of something that works for you.
ETA: the daughter who potty trained herself still wore pull-ups at night, and she kept them dry. She has grown up to be a self-controlled, decisive and self-reliant young woman.
Our son still does things randomly and doesn't seem to learn from his mistakes. He learns everything the hard way.