Is informing my mother of a secret I swore to keep, after the owner of the secret asked me to specifically inform her, considered a breach of the oath that necessitates a three-day fast?

You owe a single expiation for an oath (kaffarat yamin), because you disclosed the secret to your mother, thereby breaking your first oath. The expiation for an oath is to feed ten poor persons from the average of what you feed your own families, or to clothe them, or to free a believing slave. These options are discretionary. And for he who finds not [the means], then a fast of three days, as stated in verse 89 of Surah Al-Ma'idah.