Is it obligatory to endure the harm inflicted by the wife's sister, who conceals her possessions and discusses her problems out of fear of envy, or is it permissible to inform her of the distress caused by her actions?

If the woman is as described, then she is not sound in her thinking and in her feeling that those around her envy her. She is unfortunate and in need of help, and she should not be held accountable for her actions, but rather treated as a sick person. It is advisable to be patient with her, seeking reward from Allah, and to ask Allah for her recovery.