When a mother-in-law and daughter-in-law don't get along: The father-in-law (the MIL's husband) sees his wife hurting and in pain. The sister-in-law (the MIL's daughter) has more than likely heard all about the struggle from her mother (the MIL).
For a mother-in-law and daughter-in-law, the benefits of maintaining a close relationship cannot be overstated, as Michael Woolley and I wrote
The single most radioactive topic amongst grandparents is the tension between mothers-in-law and daughters-in-law. Once and for all: here