I agree that the DCs need assistance in alleviating anxiety.

The testing may be helpful for that.
1) The anxiety may be rooted in (or fueled by) giftedness and an ill-fitting learning environment.
2) The anxiety may be rooted in (or fueled by) a learning disability or learning difference.

G and/or the 2nd E may be important pieces to understanding and alleviating the DCs' anxiety. IMO, it is crucial to develop a trusting, supportive relationship with a professional who understands and embraces 2e kiddos before it is not possible to reach the DCs and guide their thinking.