Should I tell my married sister about her emotional relationship with her married colleague, or should I tell my mother, or what should I do?

Espionage is forbidden except to prevent an evil or avert corruption. In your case, you must advise your sister and instill in her the fear of Allah, remind her to be mindful of Him, and to uphold her husband's rights. Explain to her the prohibition of such relationships and their harms. If she repents, then conceal her secret. If she does not accept the advice, then threaten her with informing her husband or other family members who can deter her. If she still does not desist, then inform whoever can deter her.