Is it permissible to assist one's sister in spying on her husband's second wife by calling her and altering one's voice to ascertain her presence?

The fundamental principle is that spying (tajassus) is forbidden, based on the Almighty’s saying: ﴿And do not spy﴾ [49:12], and the Prophet’s (peace be upon him) saying: “O community of those who have believed with their tongues but in whose hearts faith has not entered: Do not backbite Muslims, nor pursue their faults. For whoever pursues their faults, Allah will pursue his faults. And whoever Allah pursues his faults, He will expose him even in his own house.” However, it is not considered unlawful spying if there is cause for suspicion. Thus, the second wife has the right to inquire about her husband’s travel with his other wife, and what you did was to help her know what she is entitled to, based on the obligation of drawing lots among wives for travel.