I saw my mother-in-law trying to breastfeed my baby. what should I do?

Woah firstly, that's weird. If I were you, I would go berserk. I would be so mad and not let baby anywhere near her for a while. I would definitely tell my partner and confront MIL about this. Biology aside, reckon there is some deep seeded mental/unsteadiness issues there. Just my two cents.