It does sound like a hyper-attachment issue, a form of SA.
First, the practicalities -.
Then, if he is ten years old, he has spent a lot of time developing this attachment to your wife so changing it won't be easy. You will both need to put a lot of work into this.
The first step would be to assess when he gets anxious. After five minutes? Twenty? If she steps out of the room? Does he follow her if she goes to the bathroom?
If she can't step out of the room without him following, I'd start with the Flitting Game described about ⅔ of the way down this page.
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After that, and he is relaxed and happy to wait when she is out of the room, she can step outside. But it is important that she comes back before he gets anxious. So if his tolerance is five minutes, your wife comes back in four. Repeat, repeat, repeat before stretching it to five, then six, always working at his pace. You can't resolve anxiety when he is in a state of anxiety. He isn't using his thinking brain. So this could take a lot of time.
First, the practicalities -.
Don't wait for him to let you know - take him into on a schedule, then once you know he has toileted he can snuggle in the blanket. By the way, never scold for indoor accidents, that's one reason why dogs sneak of to toilet out of sight instead of alerting their people that they need - they think its a way to avoid the negative reaction of you being cross.
Then, if he is ten years old, he has spent a lot of time developing this attachment to your wife so changing it won't be easy. You will both need to put a lot of work into this.
The first step would be to assess when he gets anxious. After five minutes? Twenty? If she steps out of the room? Does he follow her if she goes to the bathroom?
If she can't step out of the room without him following, I'd start with the Flitting Game described about ⅔ of the way down this page.

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After that, and he is relaxed and happy to wait when she is out of the room, she can step outside. But it is important that she comes back before he gets anxious. So if his tolerance is five minutes, your wife comes back in four. Repeat, repeat, repeat before stretching it to five, then six, always working at his pace. You can't resolve anxiety when he is in a state of anxiety. He isn't using his thinking brain. So this could take a lot of time.