Is it a sin to disclose information that the mother did not explicitly ask to be kept secret, but the daughter felt was a secret due to the private nature of the situation in which she was informed?

It appears that what your mother told you is a secret, as you stated, "I felt it was a secret." The fact that she spoke to you alone and was concealing it are indications that she intended it to be a secret. Acting upon such indications is agreed upon by jurists. Disclosing this secret is forbidden and entails sin if it leads to harm.