Late to the party here. Putting a 12 year old in a car seat on a plane is not merely "inadvisable"... it's downright crazy. Imagine seeing someone wearing a full rain jacket and galoshes in a swimming pool, that's how weird most people would consider the sight of a 12 year old in a car seat on a plane to be. So for those reasons I would recommend that OP not even consider it. Not for a moment.
If OP really wants some extra level of protection, I would suggest the CARES Harness. It is intended for toddlers and pre-schoolers, but at least it won't look totally crazy on a 12 year old the way that a car seat would.
https://www.amsafe.com/kidsflysafe-com/
Having said all that, I would recommend that OP and spouse seek the assistance of a therapist or other qualified professional for themselves, because there are some extremely odd and potentially harmful tendencies on display here.