A lot of people seem to have gotten off point here.
My sense is that a DIL & MIL & SIL have natural friction that is acknowledged in the Torah.
If not for the one common point that brought them together — the spouse / son / brother, they most probably would not ever come to the point of friction. Either they’d befriend one another or have nothing to do with each other.
Therefore, it is the spouse/son/brother ‘s obligation & responsibility to smooth things over. His obligation is clearly stated in the Torah — it is primarily to his wife. This takes precedance over his parents.
No one said that the DIL / MIL / SIL must love one another. However, they should act respectfully to one another.
And if the unfortunate happens & the friction arises, and a man must “choose” or take sides, it better be the side of his wife he chooses to stick by.
Because if he doesn’t, the road for him is being paved downhill, to the point where he may find that he doesn’t have a wife to stick by.