You have my sympathies . You and MIL have both learned something here . I no longer vent / rant / fight / criticize / complain via e-mail . No good has ever come of it . In fact , it has often turned a simple disagreement into World War III .
I experienced your situation with my Aunt Edna , who relentlessly criticizes other family members .
I discovered very quickly that if I made even the slightest agreeable noises or acknowledged the criticism as valid , Edna would waste no time in running to said family member , spewing out all her " helpful " ( unwanted , unwarranted and often hurtful ) advice and finish by saying " And Chibi agrees with me ! "
Needless to say , Edna and I only discuss the weather now . Any negative comments about family members are ignored , bean dipped or, failing all else , met with : "I'm not going to discuss that ."