There is a blood test that can be done Vet draws blood into a tube and you send it to whichever university does livestock testing for your area of the country. I am in southern CA and sent mine to Washington State University. The results can be emailed to you. A positive test means CAE.
There is no cure.
We had a large herd of dairy goats and blood tested every year. All kids were immediately removed and fed
heat treated colostrum. You can't pasteurize colostrum - it turns into cheese. We pasteurized all milk fed to the kids. To tell the different between pasteurized and fresh I added blue food coloring t the pasteurized milk. We showed all our goats at many shows and although they were all pasteurized we blood tested annually to make certain no CAE turned up. We had a clean herd. One year we did have an older doe who had tested clean fir several years turn positive. We taken her to a breeder. She had some positive animals although she told us she did not. Found out later that others had the same experience.

The positive doe went to the auction immediately.
This is a serious disease. The fact that your young kids are
already showing symptoms is a bad sign. CAE symptoms usually turn up at older ages.
DO NOT BREED ANY OF THESE GOATS. Unless you can guarantee pulling these kids off immediately after birth without nursing, if they get any milk or colostrum from their mama they will develop CAE.
This is a painful disease. In the worst cases of the disease the animal will not be able to walk or stand.
I'm sorry to hear about this.
However, before accepting this as CAE I recommend you do the blood test. We are not veterinarians, and can only advise as to possibilities.