LAer does have a point that comparing one child (or child by marriage) to another in a deragatory way can poison not only the relationship between parent to child but also the relationship between siblings. I know one family in which any child who misbehaved or did not meet the parents’ expectations was told, “Why can’t you behave like your sibling?” In general the children were expected to be like one another. Today the children are grown & many are married, but when they get together they often bicker & argue. Some of the siblings criticize each other, & their respective spouses, for not living the exact same lifestyle as they do.
Mrs. Beautiful’s MIL might achieve better results if she simply told her DIL “It would mean so much to me if you would call me Mommy” & leave it at that.