What should I do upon accidentally discovering that my wife curses my mother via WhatsApp with her sister, while in reality she treats my mother well?

All humans err, and the best of those who err are those who repent. So, let your anger and sorrow be for Allah. Try to rectify your wife's mistake with gentleness and kindness, and advise her with wisdom and good counsel. If the situation calls for it, explain to her that you stumbled upon the conversation by chance and were hurt, and advise her to repent. Clarify to her that her action constitutes forbidden backbiting, which is among the major sins, and instruct her to seek much forgiveness for the one she backbit. If a direct approach leads to harm, advise her indirectly, such as by speaking to her about the danger of backbiting, or by gifting her a book, or by having her listen to a lecture.