I love riddles. :)
If Carl says only a Knave (liar) would claim Betty a knave, and Betty says it is false that Alice in a knave, and knaves only lie... then Betty would have to be a knight, and since knights always tell the truth then Alice would also be a knight. Yet Alice says Carl and her are different. If she is a knight then she can only speak the truth... so that would make Carl a knave.