Is it permissible for the second wife to inform the first wife and the husband's parents of his marriage without his knowledge, and is this considered a betrayal?

If the husband does not permit his second wife to inform his first wife and his family of his marriage to her, or if informing them would lead to harm, then she is not permitted to inform them. The second wife has the right to demand her husband fulfill his duties towards her, whether they relate to justice between her and the other wife, or to maintenance, or other matters.