I believe it was her mother
The impression I got from reading various sources along the way was that Richard was supposed to be the “star” of the family, and when Karen’s voice suddenly outshone Richard’s piano and arranging talents, both Richard and their mother couldn’t handle that, and tried to keep her in her “place” creatively.
If she had been able to break free, not just from her parents, but from Richard as well, I think she could have achieved more.