Let's start with the singular first. "I stayed at my mother-in-law's house" sounds fine to me and looks OK too. So, from that, we come to either parents-in-law's house or parents-in-laws' house. Assuming you only have one sets of parents-in-law, the possessive would be parents-in-law's, wouldn't it?

Parents is plural. "I stayed at my parents' house." But if I am talking about only one parent, I say, "I stayed at my parent's house."


TEd