Why does the Gemara mention the story about the mother -in-law/daughter -in- law the way it does. If it wanted to illustrate the danger, it could have described the events without adding that the mother in law despised her daughter in law. Is there a further meaning to this?
It has significant Halachic ramifications, as the Mishnah states clearly in Yevamos (117a). While one witness is believed to testify that a woman's husband was killed overseas (and the woman becomes permitted to someone else and is not an Agunah), if that one witness is the woman's mother-in-law, she is not believed, because the mother-in-law is assumed to have malicious intent (she wants the daughter-in-law to marry another man while her husband is really alive somewhere, so that her new marriage will be an act of adultery for which she will be liable to death when her husband shows up). Likewise, if that one witness is her daughter-in-law, she is not believed.
As to the reason for this hatred, see Rashi in Yevamos (117a, DH v'Yevamtah) and the other Rishonim there.
The Gemara here may also be relating this story as a piece of practical advice. It may sometimes be worthwhile to beware of one's mother-in-law.
All the best,